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European Mathematical Society Publishing House
2024-03-29 07:43:05
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https://www.ems-ph.org/meta/jmeta-stream.php?jrn=PRIMS&vol=33&update_since=2024-03-29
Publications of the Research Institute for Mathematical Sciences
Publ. Res. Inst. Math. Sci.
PRIMS
0034-5318
1663-4926
General
10.4171/PRIMS
http://www.ems-ph.org/doi/10.4171/PRIMS
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European Mathematical Society Publishing House
Zuerich, Switzerland
© Research Institute for Mathematical Sciences, Kyoto University
33
1997
1
Hodge Theory and the Art of Paper Folding
Michael
Kapovich
University of California at Davis, DAVIS, UNITED STATES
John
Millson
University of Maryland, COLLEGE PARK, UNITED STATES
Using Hodge theory and L2-cohomology we study the singularities and topology of configuration and moduli spaces of polygonal linkages in the 2-sphere. As a consequence we describe the local deformation space of a folded paper cone in R3.
Geometry
General
1
31
10.2977/prims/1195145531
http://www.ems-ph.org/doi/10.2977/prims/1195145531
Theory of Prehomogeneous Vector Spaces, II, A Supplement
Akihiko
Gyoja
Kyoto University, KYOTO, JAPAN
Algebraic geometry
General
33
57
10.2977/prims/1195145532
http://www.ems-ph.org/doi/10.2977/prims/1195145532
Second Order Perturbation Bounds
Vikas
Bist
Panjab University, CHANDIGARH, INDIA
Harkrishan
Vasudeva
Panjab University, CHANDIGARH, INDIA
With a view to studying perturbation bounds, the class of functions f for which ∥df(A)∥ = ∥ f(1)(A)∥ and ∥d(2)f(A)∥ = ∥ f(2)(A)∥, where dkf(A) (respectively fk(A)) denotes the k-th Frechet (ordinary) derivative, k=1,2, has been investigated.
Operator theory
General
59
71
10.2977/prims/1195145533
http://www.ems-ph.org/doi/10.2977/prims/1195145533
Poisson Cohomology of Plane Quadratic Poisson Structures
Nobutada
Nakanishi
Gifu Keizai University, OGAKI-SHI, JAPAN
Global analysis, analysis on manifolds
General
73
89
10.2977/prims/1195145534
http://www.ems-ph.org/doi/10.2977/prims/1195145534
Generalization and Exact Deformations of Quantum Groups
Christian
Frønsdal
University of California, LOS ANGELES, UNITED STATES
A large family of "standard" coboundary Hopf algebras is investigated. The existence of a universal R-matrix is demonstrated for the case when the parameters are in general position. Algebraic surfaces in parameter space are characterized by the appearance of certain ideals; in this case the universal R-matrix exists on the associated algebraic quotient. In special cases the quotient is a "standard" quantum group; all familiar quantum groups including twisted ones are obtained in this way. In other special cases one finds new types of coboundary bi-algebras. The "standard" universal R-matrix is shown to be the unique solution of a very simple, linear recursion relation. The classical limit is obtained in the case of quantized Kac-Moody algebras of finite and affine type. Returning to the general case, we study deformations of the standard R-matrix and the associated Hopf algebras. A preliminary investigation of the first order deformations uncovers a class of deformations that incompasses the quantization of all Kac-Moody algebras of finite and affine type. The corresponding exact deformations are described as generalized twists, R∊ = (Ft)–1RF, where R is the standard R-matrix and the cocycle F (a power series in the deformation parameter ∊) is the solution of a linear recursion relation of the same type as that which determines R. Included here is the universal R-matrix for the elliptic quantum groups associated with sl(n), a big surprise! Specializing again, to the case of quantized Kac-Moody algebras, and taking the classical limit of these esoteric quantum groups, one re-discovers all the trigonometric and elliptic r-matrices of Belavin and Drinfeld. The formulas obtained here are easier to use than the original ones, and the structure of the space of classical r-matrices is more transparent. The r-matrices obtained here are more general in that they are defined on the full Kac-Moody algebras, the central extensions of the loop groups.
Algebraic geometry
General
91
149
10.2977/prims/1195145535
http://www.ems-ph.org/doi/10.2977/prims/1195145535
On p-Adic Zeta-Functions Associated to the Positive Topology of Algebraic Number Fields
Alexander
Schmidt
Universität Heidelberg, HEIDELBERG, GERMANY
Number theory
General
151
166
10.2977/prims/1195145536
http://www.ems-ph.org/doi/10.2977/prims/1195145536
Local Uniqueness in the Cauchy Problem for Second Order Elliptic Equations with Non-Lipschitzian Coefficients
Shigeo
Tarama
Kyoto University, KYOTO, JAPAN
We show the local uniqueness of the Cauchy problem for the second order elliptic operators whose coefficients of the principal part are real-valued and continuous with some modulus of continuity. These coefficients are not necessarily lipschitz continuous. The proof is given by drawing the Carleman estimates with a weight attached to the modulus of continuity.
Partial differential equations
General
167
188
10.2977/prims/1195145537
http://www.ems-ph.org/doi/10.2977/prims/1195145537
2
Fourier Transform for Paragroups and Its Application to the Depth Two Case
Nobuya
Sato
University of Tokyo, TOKYO, JAPAN
We prove that the flatness condition in Ocneanu's paragroup theory for graphs with depth two is equivalent to existence of the multiplicative unitaries in the theory of Baaj-Skandalis by using "Fourier transform" introduced by A. Ocneanu. Moreover, from two Kac algebras dual to each other, we construct a subfactor as a crossed product by a Kac algebra action, with the string algebra construction.
Functional analysis
General
189
222
10.2977/prims/1195145447
http://www.ems-ph.org/doi/10.2977/prims/1195145447
Short Time Asymptotic Behaviour and Large Deviation for Brownian Motion on Some Affine Nested Fractals
Takashi
Kumagai
Kyoto University, KYOTO, JAPAN
We study so called Varadhan type short time asymptotic estimates of heat kernels and Shilder type large deviation for Brownian motion on some affme nested fractals introduced in [7]. As a corollary to our approach, we obtain sharper estimates of heat kernels for a class of one dimensional diffusion processes studied in [8].
Probability theory and stochastic processes
General
223
240
10.2977/prims/1195145448
http://www.ems-ph.org/doi/10.2977/prims/1195145448
Topological Tensor Products of Unbounded Operator Algebras on Frechet Domains
Wolf-Dieter
Heinrichs
Technische Universität Dresden, DRESDEN, GERMANY
The aim of this paper is to investigate topological properties of unbounded operator algebras A⊂L+(D) and its stability under the formation of topological tensor products A1 ⊗aA2. It is used the method to define topological properties by operator.
Operator theory
General
241
255
10.2977/prims/1195145449
http://www.ems-ph.org/doi/10.2977/prims/1195145449
On Uniqueness of Commutative Rings of Weyl Group Invariant Differential Operators
Kenji
Taniguchi
University of Tokyo, TOKYO, JAPAN
The uniqueness of commutative rings of classical Weyl group invariant differential operators is discussed. We show this uniqueness for trigonometric or elliptic potential cases under some order conditions. For rational potential cases, counter examples are constructed.
Global analysis, analysis on manifolds
General
257
276
10.2977/prims/1195145450
http://www.ems-ph.org/doi/10.2977/prims/1195145450
Quantum Current Operators-I Zeros and Poles of Quantum Current Operators and the Condition of Quantum Integrability
Jintai
Ding
Kyoto University, KYOTO, JAPAN
Tetsuji
Miwa
Kyoto University, KYOTO, JAPAN
For the current realization of the affine quantum groups, a simple comultiplication for the quantum current operators was given by Drinfeld. With this comultiplication, we study the zeros and poles of the quantum current operators and present a condition of integrability on the quantum current operators of Uq(sl^(2)), which is a deformation of the corresponding condition for sl^(2). We also present the results about the zeros and poles of the quantum current operators of Uq(sl^(n)).
Nonassociative rings and algebras
General
277
284
10.2977/prims/1195145451
http://www.ems-ph.org/doi/10.2977/prims/1195145451
Quantum Current Operators-II Difference Equations of Quantum Current Operators and Quantum Parafermion Construction
Jintai
Ding
Kyoto University, KYOTO, JAPAN
Boris
Feigin
Independent University of Moscow, MOSCOW, RUSSIAN FEDERATION
For the current realization of the affine quantum groups, a simple comultiplication for the quantum current operators was given by Drinfeld. With this comultiplication, we prove that, for the integrable modules of Uq(sl^(2)) of level k + 1, x±(z)x±(zq±2) ⋯ x±(zq±2k) are vertex operators satisfying certain q-difference equations, and we derive the quantum parafermions of Uq(sl^(2)).
Nonassociative rings and algebras
General
285
300
10.2977/prims/1195145452
http://www.ems-ph.org/doi/10.2977/prims/1195145452
Extended Affine Root Systems III (Elliptic Weyl Groups)
Kyoji
Saito
Kyoto University, KYOTO, JAPAN
Tadayoshi
Takebayashi
Waseda University, TOKYO, JAPAN
We give a presentation of an elliptic Weyl group W(R) (=the Weyl group for an elliptic root system*) R) in terms of the elliptic Dynkin diagram Γ(R, G) for the elliptic root system. The presentation is a generalization of a Coxeter system: the generators are in one to one correspondence with the vertices of the diagram and the relations consist of two groups : i) elliptic Coxeter relations attached to the diagram, and ii) a flniteness condition on the Coxeter transformation attached to the diagram. The group defined only by the elliptic Coxeter relations is isomorphic to the central extension W(R, G) of W(R) by an infinite cyclic group, called the hyperbolic extension of W(R). *) an elliptic root system=a 2-extended affine root system (see the introduction and the remark at its end).
Group theory and generalizations
General
301
329
10.2977/prims/1195145453
http://www.ems-ph.org/doi/10.2977/prims/1195145453
3
A Note on the Approximation Entropies of Certain Shifts
Kiichi
Nishiuchi
University of Tokyo, TOKYO, JAPAN
Voiculescu has proposed several routes to quantum entropies. Among them, the notion of the "approximation entropies" is a group of four entropies with similar definitions, based on two kinds of approximations. The C*-cases are extensions of the classical topological entropy and the W*-cases are those of the measure-theoretic one. In this paper, we will focus on the approximation entropies and investigate the entropies of Powers' binary shifts with some condition and the Jones shifts.
Functional analysis
General
331
339
10.2977/prims/1195145318
http://www.ems-ph.org/doi/10.2977/prims/1195145318
Scattering Theory for Elastic Wave Propagation Problems in Perturbed Stratified Media II
Senjo
Shimizu
Shizuoka University, SHIZUOKA, JAPAN
We consider a self-adjoint operator governing the propagation of elastic waves in stratified media R3, where Lame functions and a density are perturbed in a compact region. In this paper we prove the existence, the completeness, and the invariance principle of wave operators associated with the self-adjoint operator and a self-adjoint operator governing the propagation of elastic waves in unperturbed stratified media R3. The proof is based on an abstract scattering theory due to M. S. Birman.
Partial differential equations
General
341
358
10.2977/prims/1195145319
http://www.ems-ph.org/doi/10.2977/prims/1195145319
Normal Quintic Surfaces which are Birationally Enriques Surfaces
Yumiko
Umezu
Toho University, TOKYO, JAPAN
Algebraic geometry
General
359
384
10.2977/prims/1195145320
http://www.ems-ph.org/doi/10.2977/prims/1195145320
On the Relation between Tautly Imbedded On the Relation between Tautly Imbedded Space Modulo an Analytic Subset S and Hyperbolically Imbedded Space Modulo S
Yukinobu
Adachi
12-29 Kurakuen 2ban-cho, HYOGO, JAPAN
Several complex variables and analytic spaces
General
385
392
10.2977/prims/1195145321
http://www.ems-ph.org/doi/10.2977/prims/1195145321
The Mumford-Tate Conjecture for Drinfeld-Modules
Richard
Pink
ETH Zürich, ZÜRICH, SWITZERLAND
Consider the Galois representation on the Tate module of a Drinfeld module over a finitely generated field in generic characteristic. The main object of this paper is to determine the image of Galois in this representation, up to commensurability. We also determine the Dirichlet density of the set of places of prescribed reduction type, such as places of ordinary reduction.
Number theory
General
393
425
10.2977/prims/1195145322
http://www.ems-ph.org/doi/10.2977/prims/1195145322
Normal Algebraic Surfaces with Trivial Tricanonical Divisors
De-Qi
Zhang
Osaka University Graduate School of Science, OSAKA, JAPAN
We prove that upto isomorphisms there are at least one and at most three rational log Enriques surfaces of index 3 and Type A17.
Algebraic geometry
General
427
442
10.2977/prims/1195145323
http://www.ems-ph.org/doi/10.2977/prims/1195145323
Operator Convex Functions of Several Variables
Frank
Hansen
University of Copenhagen, COPENHAGEN, DENMARK
The functional calculus for functions of several variables associates to each tuple x = (x1, ⋯, xk) of selfadjoint operators on Hilbert spaces H1, ⋯,Hk an operator f(x) in the tensor product B(H1)⊗ ⋯ ⊗B(Hk). We introduce the notion of generalized Hessian matrices associated with f. Those matrices are used as the building blocks of a structure theorem for the second Fréchet differential of the map x → f(x). As an application we derive that functions with positive semi-definite generalized Hessian matrices of arbitrary order are operator convex. The result generalizes a theorem of Kraus [15] for functions of one variable.
Real functions
General
443
463
10.2977/prims/1195145324
http://www.ems-ph.org/doi/10.2977/prims/1195145324
Connectedness of the Fibers of a Liouvillian Function
Emmanuel
Paul
Université Paul Sabatier, TOULOUSE CEDEX, FRANCE
Let D be a normal crossing divisor in a complex analytic manifold of dimension n, and let Ω be a closed logarithmic one-form, with poles on D. Under appropriate hypothesis, we prove the connectedness of the fibers for a primitive of Ω in "good" neighborhoods of D. We deduce the connectedness of the fibers of Liouvillian functions of type f= f1λ 1 ⋯ fpλp at the origin of Cn, under two conditions: the first extends the usual notion that "f is not a power". The second excludes certain meromorphic functions.
Several complex variables and analytic spaces
General
465
481
10.2977/prims/1195145325
http://www.ems-ph.org/doi/10.2977/prims/1195145325
On Certain Multiple Bailey, Rogers and Dougall Type Summation Formulas
Jan
van Diejen
University of Montréal, MONTRÉAL, QC, CANADA
A multidimensional generalization of Bailey's very-well-poised bilateral basic hypergeometric 6⒖ summation formula and its Dougall type 5H5 hypergeometric degeneration for q → 1 is studied. The multiple Bailey sum amounts to an extension corresponding to the case of a nonreduced root system of certain summation identities associated to the reduced root systems that were recently conjectured by Aomoto and Ito and proved by Macdonald. By truncation, we obtain multidimensional analogues of the very-well poised unilateral (basic) hypergeometric Rogers 6◁ and Dougall 5F4 sums (both nonterminating and terminating). The terminating sums may be used to arrive at product formulas for the norms of recently introduced (q-)Racah polynomials in several variables.
Special functions
General
483
508
10.2977/prims/1195145326
http://www.ems-ph.org/doi/10.2977/prims/1195145326
4
Solvability of Equations for Motion of a Vortex Filament with or without Axial Flow
Atusi
Tani
Tokyo Institute of Technology, TOKYO, JAPAN
Takahiro
Nishiyama
Keio University, YOKOHAMA, JAPAN
It is known that the motion of a vortex filament with axial flow in a perfect fluid is approximately described by a generalization of the localized induction equation. The unique solvability of the initial value problem for it is first established by parabolic regularization. As the axial flow effect vanishes, its solution converges to that of the localized induction equation. Analogous results are obtained in the spatially periodic case.
Partial differential equations
General
509
526
10.2977/prims/1195145146
http://www.ems-ph.org/doi/10.2977/prims/1195145146
Semialgebraic Description of Teichmiiller Space
Yohei
Komori
Osaka City University, OSAKA, JAPAN
We give a concrete semialgebraic description of Teichmiiller space Tg of the closed surface group Γg of genus g(≥ 2). Our result implies that for any SL2(R)-representation of Γg, we can determine whether this representation is discrete and faithful or not by using 4g—6 explicit trace inequalities. We also show the connectivity and contractibility of Tg from the point of view of SL2(R)-representations of Γg. Previously, these properties of Tg had been proved by using hyperbolic geometry and quasi-conformal deformations of Fuchsian groups. Our method is simple and only uses topological properties of the space of SL2(R)-representations of Γg.
Algebraic geometry
General
527
571
10.2977/prims/1195145147
http://www.ems-ph.org/doi/10.2977/prims/1195145147
A Family of Rank-2 Mathematical Instanton Bundles on P3
Valery
Vedernikov
, MOSCOW K-30, RUSSIAN FEDERATION
A big family of rank-2 mathematical instanton bundles on the three-dimensional complex projective space P3 is constructed.
Algebraic geometry
General
573
598
10.2977/prims/1195145148
http://www.ems-ph.org/doi/10.2977/prims/1195145148
Goursat Problem for a Microdifferentlal Operator of Fuchsian Type and Its Application
Susumu
Yamazaki
University of Tokyo, TOKYO, JAPAN
We consider a matrix of microdifferential operators of Fuchsian type with respect to several variables and obtain the Cauchy-Kovalevskaja type theorem for the Goursat problem. Moreover, we prove the existence theorem in the framework of microfunctions under some assumptions for initial values and the operator.
Several complex variables and analytic spaces
General
599
641
10.2977/prims/1195145149
http://www.ems-ph.org/doi/10.2977/prims/1195145149
Monodromy at Infinity and Fourier Transform
Claude
Sabbah
Ecole Polytechnique, PALAISEAU CEDEX, FRANCE
Let f:U→U be a regular function on a smooth quasi-projective variety U. We compute the limit mixed Hodge structure (when t→ ∞) of the cohomology of the fibers f= t in terms of the Fourier transform of the Gauss-Manin system associated to f.
Algebraic geometry
General
643
685
10.2977/prims/1195145150
http://www.ems-ph.org/doi/10.2977/prims/1195145150
Analytic Discs Attached to Manifolds with Boundary
Luca
Baracco
Università di Padova, PADOVA, ITALY
Giuseppe
Zampieri
Università di Padova, PADOVA, ITALY
Several complex variables and analytic spaces
General
687
694
10.2977/prims/1195145151
http://www.ems-ph.org/doi/10.2977/prims/1195145151
The Cut-Off Phenomenon for Random Walks on Hamming Graphs with Variable Growth Conditions
Akihito
Hora
Kyoto University, KYOTO, JAPAN
The cut-off phenomenon is a remarkable critical phenomenon observed in the process of convergence to equilibrium in a wide variety of Markov chains. Diaconis-Graham-Morrison [3] established the first precise evaluation around the critical time for Ehrenfests' urn model concerning 2 urns and d balls, i.e. nearest neighbor random walks on hypercube Zd
Probability theory and stochastic processes
General
695
710
10.2977/prims/1195145152
http://www.ems-ph.org/doi/10.2977/prims/1195145152
A Correction to: 'Operator Convex Functions of Several Variables'
Frank
Hansen
University of Copenhagen, COPENHAGEN, DENMARK
Several complex variables and analytic spaces
General
711
711
10.2977/prims/1195145153
http://www.ems-ph.org/doi/10.2977/prims/1195145153
5
The Exactness Theorem for Floer Homology
Hong-Yu
Wang
National University of Singapore, SINGAPORE, SINGAPORE
In this article, we study a long exact sequence relating the mstanton homology of two homology 3-spheres which are obtained from each other by ± 1 -surgery. We prove that the long exact sequence, via a short exact sequence of chain complex, is the same as the sequence defined by the exact triangle of cobordisms introduced by Floer.
Manifolds and cell complexes
General
713
750
10.2977/prims/1195145014
http://www.ems-ph.org/doi/10.2977/prims/1195145014
An Upper Bound for the Characteristic Variety of an Induced D-Module
Carlos
Menezes
Universidade do Porto, PORTO, PORTUGAL
We generalise the Carzy (M) upper bound of Laurent & Schapira [LS87] for the characteristic variety of the induced system of a coherent Dx-module M on a hypersurface Y of X to the case where Y is a smooth submanifold of X of arbitrary codimension.
Global analysis, analysis on manifolds
General
751
764
10.2977/prims/1195145015
http://www.ems-ph.org/doi/10.2977/prims/1195145015
Strongly Hyperbolic Systems of Maximal Rank
Tatsuo
Nishitani
Kyoto University, KYOTO, JAPAN
Partial differential equations
General
765
773
10.2977/prims/1195145016
http://www.ems-ph.org/doi/10.2977/prims/1195145016
Gevrey Hypoellipticity for Grushin Operators
Tadato
Matsuzawa
Meijo University, NAGOYA, AICHI, JAPAN
Partial differential equations
General
775
799
10.2977/prims/1195145017
http://www.ems-ph.org/doi/10.2977/prims/1195145017
Nonlinear Singular First Order Partial Differential Equations Whose Characteristic Exponent Takes a Positive Integral Value
Hideshi
Yamane
University of Tokyo, TOKYO, JAPAN
We consider nonlinear singular partial differential equations of the form (tDt–ρ(x))u = ta(x)+G2(x)(t, tDtu, u, D1u,...,Dnu). It has been proved by Gerard and Tahara that there exists a unique holomorphic solution with u(0, x) ≡ 0 if the characteristic exponent ρ(x) avoids positive integral values. In the present paper we consider what happens if ρ(x) takes a positive integral value at x=0. Genetically, the solution u(t, x) is singular along the analytic set {t=0, ρ(x) ∈ N*}, N*={1, 2,...}, and we investigate how far it can be analytically continued.
Partial differential equations
General
801
811
10.2977/prims/1195145018
http://www.ems-ph.org/doi/10.2977/prims/1195145018
Multiple Gamma Functions and Multiple q-Gamma Functions
Kimio
Ueno
Waseda University, TOKYO, JAPAN
Michitomo
Nishizawa
Waseda University, TOKYO, JAPAN
We give an asymptotic expansion (the higher Stirling formula) and an infinite product representation (the Weierstrass canonical product representation) of the Vigneras multiple gamma functions by considering the classical limit of the multiple q-gamma functions.
Special functions
General
813
838
10.2977/prims/1195145019
http://www.ems-ph.org/doi/10.2977/prims/1195145019
Finite-Dimensional Representations of Quantum Affine Algebras
Tatsuya
Akasaka
International Institute for Advanced Studies, KYOTO, JAPAN
Masaki
Kashiwara
Kyoto University, KYOTO, JAPAN
We present a conjecture on the irreducibility of the tensor products of fundamental representations of quantized affme algebras. This conjecture implies in particular that the irreducibility of the tensor products of fundamental representations is completely described by the poles of R-matrices. The conjecture is proved in the cases of type An(1) and Cn(1).
Nonassociative rings and algebras
General
839
867
10.2977/prims/1195145020
http://www.ems-ph.org/doi/10.2977/prims/1195145020
6
Squeezing of Optical States on the CCR-Algebra
Reinhard
Honegger
Universität Tübingen, TÜBINGEN, GERMANY
Alfred
Rieckers
Universität Tübingen, TÜBINGEN, GERMANY
Squeezing processes are commonly described in terms of quadratic Hamiltonians, which generate unitary implementations of Bogoliubov transformations of the quantized electromagnetic field. Here the behaviour of the quasifree, the classical, and the coherent photon states under general squeezing Bogoliubov transformations is investigated. It is found that there is a great variety of mixed classical states, which remain classical under the squeezing operation, whereas each pure classical state becomes non-classical. Especially, some classical, microscopic first order coherent states remain classical and coherent of first order under one-mode squeezing. This contrasts squeezing of macroscopic coherent states.
Quantum theory
General
869
892
10.2977/prims/1195144880
http://www.ems-ph.org/doi/10.2977/prims/1195144880
Images Directes de Fibres en Droites Adjoints
Christophe
Mourougane
Institut de Recherche Mathématiques de Rennes (IRMAR), RENNES, FRANCE
Our main purpose is to study ampleness and positivity properties of the direct image φ ⋆L of a holomorphic line bundle L under a smooth morphism φ: X → Y between compact complex analytic manifolds. We show that in general the ampleness of L does not imply that of the direct image φ ⋆L but only that of thé direct image of the adjoint line bundle (φ ⋆(KX/Y/i> ⊗L).
Algebraic geometry
General
893
916
10.2977/prims/1195144881
http://www.ems-ph.org/doi/10.2977/prims/1195144881
Representations of Hermitian Kernels by Means of Krein Spaces
Tiberiu
Constantinescu
University of Texas at Dallas, RICHARDSON, UNITED STATES
Aurelian
Gheondea
Bilkent University, BILKENT, ANKARA, TURKEY
Hermitian kernels are studied as generalizations of kernels of positive type. The main tool is the axiomatic concept of induced Krem space. The existence of Kolmogorov decompositions of a hermitian kernel and their uniqueness, modulo unitary equivalence, are characterized. The existence of reproducing kernel Krein spaces is shown to be equivalent to the existence of Kolmogorov decompositions. Applications Applications to the Naimark dilations of Toeplitz hermitian kernels on the set of integers and to the uniqueness of the Krem space completions of nondegenerate inner product spaces are included.
Functional analysis
General
917
951
10.2977/prims/1195144882
http://www.ems-ph.org/doi/10.2977/prims/1195144882
A Complex Analytic Study on the Theory of Fourier Series on Compact Lie Groups
Yutaka
Saburi
Chiba Jr. College, ICHIKAWA, JAPAN
The characterization of Fourier series of real analytic functions and hyperfunctions on compact Lie groups is discussed by means of complex analysis.
Topological groups, Lie groups
General
953
966
10.2977/prims/1195144883
http://www.ems-ph.org/doi/10.2977/prims/1195144883
1-Cocycles for Rotationally Invariant Measures
Hiroaki
Shimomura
, TOKYO, JAPAN
Probability theory and stochastic processes
General
967
985
10.2977/prims/1195144884
http://www.ems-ph.org/doi/10.2977/prims/1195144884
On the Thomae Formula for ZN Curves
Atsushi
Nakayashiki
Kyushu University, FUKUOKA, JAPAN
We shall give an elementary and rigorous proof of the Thomae formula for b>ZN curves which was discovered by Bershadsky and Radul [1, 2]. Instead of using the determinant of the Laplacian we use the traditional variational method which goes back to Riemann, Thomae, Fuchs. In the proof we made explicit the algebraic expression of the chiral Szego kernels and prove the vanishing of zero values of derivatives of theta functions with b>ZN invariant 1/2N characteristics.
Algebraic geometry
General
987
1015
10.2977/prims/1195144885
http://www.ems-ph.org/doi/10.2977/prims/1195144885