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European Mathematical Society Publishing House
2024-03-28 16:12:57
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https://www.ems-ph.org/meta/jmeta-stream.php?jrn=PRIMS&vol=36&update_since=2024-03-28
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
36
2000
1
Conjugacy of Z2-subshifts and Textile Systems
Hiroshi
Aso
Kyushu University, FUKUOKA, JAPAN
It will be shown that any topological conjugacy of Z2-subshifts is factorized into a finite number of bipartite codes, and that in particular when textile shifts which are Z2-subshifts arising from textile systems introduced by Nasu are taken each bipartite code appearing in this factorization is given by a bipartite graph code of textile shifts which is defined in terms of textile systems. The latter result extends the Williams result on strong shift equivalence of Z'-topological Markov shifts to a Z2-shift case.
Global analysis, analysis on manifolds
General
1
18
10.2977/prims/1195143225
http://www.ems-ph.org/doi/10.2977/prims/1195143225
Derived Categories for Functional Analysis
Fabienne
Prosmans
Université de Paris XIII/CNRS, VILLETANEUSE, FRANCE
Homological methods for functional analysis, derived projective and inductive limits, pro-objects, non-abelian homological algebra, quasi-abelian categories
In this paper, we study the homological algebra of the category Tc of locally convex topological vector spaces from the point of view of derived categories. We start by showing that Tc is a quasi-abelian category in which products and direct sums are exact. This allows us to derive projective and inductive limit functors and to clarify their homological properties. In particular, we obtain strictness and acyclicity criteria. Next, we establish that the category formed by the separated objects of Jc is quasi-abelian and has the same derived category as Tc. Since complete objects of Tc do not form a quasi-abelian category, we are lead to introduce the notion of cohomological completeness and to study the derived completion functor. Our main result in this context is an equivalence between the subcategory of D(Tc) formed by cohomologically complete complexes and the derived category of the category of pro-Banach spaces. We show also that, under suitable assumptions, we can reduce the computation of Ext's in Tc to their computation in 'Ban by means of derived projective limits. We conclude the paper by studying derived duality functors.
Functional analysis
Category theory; homological algebra
General
19
83
10.2977/prims/1195143226
http://www.ems-ph.org/doi/10.2977/prims/1195143226
The Meromorphic Solutions of the Bruschi–Calogero Equation
Nariya
Kawazumi
University of Tokyo, TOKYO, JAPAN
Youichi
Shibukawa
Hokkaido University, SAPPORO, JAPAN
We give all the meromorphic functions defined near the origin 0 ∈ ℂ satisfying a functional equation investigated by Bruschi and Calogero [1], [2].
Global analysis, analysis on manifolds
Special functions
Partial differential equations
General
85
109
10.2977/prims/1195143227
http://www.ems-ph.org/doi/10.2977/prims/1195143227
Elliptic Root System and Elliptic Artin Group
Hiroshi
Yamada
Kitami Institute of Technology, KITAMI, HOKKAIDO, JAPAN
Algebraic geometry
General
111
138
10.2977/prims/1195143228
http://www.ems-ph.org/doi/10.2977/prims/1195143228
Operator Differentiable Functions
Gert
Pedersen
University of Copenhagen, COPENHAGEN, DENMARK
C*-algebra, Fréchet derivative, operator differentiability, commutator equations
We study the Banach *-algebra C1QP(I) of C1-functions on the compact interval I such that the corresponding Hilbert space operator function T → f(T), for T = T* and sp(T) ⊂ I, is Fréchet differentiable. If f(x) = ∫ eitx f^(t)dt we know that the differential is given by the formula dfT(S) = ∫-∞∞ ∫01 UstSU(1-s)t dsf'^(t) dt, where Ut = exp(itT). Functions of this type are dense in C1QP(I), and C2(I) ⊂ C1QP(I) ⊂ C1(I), so several classical results can be deduced. In particular we show that if T ∈ D(δ), where δ is the generator of a one-parameter group of *-automorphisms of a C*-algebra A (or just a closed *-derivation in A), then f(T) ∈ D(δ) for every f in C1QP(I), sp(T) ⊂ I, and δ(f(T)) = dfT(δ(T)).
Functional analysis
Operator theory
General
139
157
10.2977/prims/1195143229
http://www.ems-ph.org/doi/10.2977/prims/1195143229
2
Representation Varieties and Character Varieties
Kazunori
Nakamoto
Kyoto University, KYOTO, JAPAN
Algebraic geometry
Number theory
Associative rings and algebras
Group theory and generalizations
159
189
10.2977/prims/1195143100
http://www.ems-ph.org/doi/10.2977/prims/1195143100
Cauchy Problems for Mixed-Type Operators
Keisuke
Uchikoshi
National Defense Academy of Japan, YOKOSUKA, KANAGAWA, JAPAN
We give a general theory of the Cauchy problems for various types of operators, containing hyperbolic operators, elliptic operators, and mixed-type operators. We will give a necessary and sufficient condition for the Cauchy problems to be well-posed.
Partial differential equations
General
191
230
10.2977/prims/1195143101
http://www.ems-ph.org/doi/10.2977/prims/1195143101
Harmonic Function Spaces of Probability Measures on Fusion Algebras
Tomohiro
Hayashi
Tohoku University, SENDAI, JAPAN
In this note, we study harmonic function spaces of probability measures on fusion algebras of C*-tensor categories and show that almost ergodicity is equivalent to ergodicity for amenable fusion algebras, which generalizes a result due to S. Popa for probability measures associated to subfactors.
Functional analysis
General
231
252
10.2977/prims/1195143102
http://www.ems-ph.org/doi/10.2977/prims/1195143102
Schur Products and Module Maps on B(ℋ)
Takashi
Itoh
Gunma University, GUNMA, JAPAN
Masaru
Nagisa
Chiba University, CHIBA, JAPAN
We describe the isometry which induces a Schur product on B(ℋ) and characterize Schur product maps as completely bounded module maps from K(ℋ) to B(ℋ).
Functional analysis
Operator theory
General
253
268
10.2977/prims/1195143103
http://www.ems-ph.org/doi/10.2977/prims/1195143103
The First Fundamental Theorem of Coinvariant Theory for the Quantum General Linear Group
Kenneth
Goodearl
University of California, SANTA BARBARA, UNITED STATES
Thomas
Lenagan
University of Edinburgh, EDINBURGH, UNITED KINGDOM
Laurent
Rigal
Université Jean-Monnet, SAINT-ETIENNE CEDEX 2, FRANCE
We prove First Fundamental Theorems of Coinvariant Theory for the standard coactions of the quantum groups Oq(GLt(K)) and Oq(SLt(K)) on the quantized algebra Oq(Mm,t(K)) ⊗ Oq(Mt, n(K)). (Here K is an arbitrary field and q an arbitrary nonzero scalar.) In both cases, the set of co-invariants is a subalgebra of Oq(Mm,t(K)) ⊗ Oq(Mt, n(K)), which we identify.
Associative rings and algebras
Nonassociative rings and algebras
General
269
296
10.2977/prims/1195143104
http://www.ems-ph.org/doi/10.2977/prims/1195143104
On the Exact WKB Analysis of Second Order Linear Ordinary Differential Equations with Simple Poles
Tatsuya
Koike
Kyoto University, KYOTO, JAPAN
Ordinary differential equations
General
297
319
10.2977/prims/1195143105
http://www.ems-ph.org/doi/10.2977/prims/1195143105
3
Codimension Two Compact Hausdorff Foliations by Hyperbolic Surfaces Are Not Stable
Kazuhiko
Fukui
Kyoto Sangyo University, KYOTO, JAPAN
Atsuhide
Mori
Kyoto Sangyo University, KYOTO, JAPAN
Manifolds and cell complexes
General
321
336
10.2977/prims/1195142950
http://www.ems-ph.org/doi/10.2977/prims/1195142950
Real Forms of the Radon–Penrose Transform
Andrea
D'Agnolo
Università di Padova, PADOVA, ITALY
Corrado
Marastoni
Università di Padova, PADOVA, ITALY
The complex Radon correspondence relates an n-dimensional projective space with the Grassmarm manifold of its p-dimensional planes. This is the geometric background of the Radon–Penrose transform, which intertwines cohomology classes of homogeneous line bundles with holomorphic solutions to the generalized massless field equations. A good framework to deal with such problems is provided by the recently developed theory of integral transforms for sheaves and D-modules. In particular, an adjunction formula describes the range of transforms acting on general function spaces, associated with constructible sheaves. The linear group SL(n + 1,C) naturally acts on the Radon correspondence. A distinguished family of function spaces is then the one associated with locally constant sheaves along the closed orbits of the real forms of SL(n + 1,C). In this paper, we systematically apply the above-mentioned adjunction formula to such function spaces. We thus obtain in a unified manner several results concerning the complex, conformal, or real Radon transforms.
Partial differential equations
Several complex variables and analytic spaces
Integral transforms, operational calculus
General
337
383
10.2977/prims/1195142951
http://www.ems-ph.org/doi/10.2977/prims/1195142951
Extended Affine Root System IV (Simply-Laced Elliptic Lie Algebras)
Kyoji
Saito
Kyoto University, KYOTO, JAPAN
Daigo
Yoshii
Kyoto University, KYOTO, JAPAN
Let (R, G) be a pair consisting of an elliptic root system R and a marking G of R. Assume that the attached elliptic Dynkin diagram Γ(R, G) is simply-laced. To the simply-laced elliptic root system, we associate three Lie algebras, explained in 1), 2) and 3) below. The main result of the present paper is to show that all three algebras are isomorphic. The first one, studied in §3, is the subalgebra g(R) generated by the highest vector eα for all α ∈ R in the quotient Lie algebra VQ(R) / DVQ(R) of the lattice vertex algebra attached to the elliptic root lattice Q(R). The second algebra e(Γell), studied in §4, is presented by the Chevalley generators and the generalized Serre relations attached to the elliptic Dynkin diagram Γell = Γ(R, G) The third algebra ℌZ'af * gaf, studied in §5, is defined as an amalgamation of an affine Heisenberg algebra and an affine Kac–Moody algebra together with the finite amalgamation relations.
Nonassociative rings and algebras
General
385
421
10.2977/prims/1195142952
http://www.ems-ph.org/doi/10.2977/prims/1195142952
Blowing Ups of 3-dimensional Terminal Singularities, II
Takayuki
Hayakawa
Kanazawa University, KANAZAWA, JAPAN
We study blowing ups of 3-dimensional terminal singularities of type (cD/2) such that the exceptional loci are prime divisors and have discrepancies 1/2. We determined such blowing ups completely.
Algebraic geometry
Several complex variables and analytic spaces
General
423
456
10.2977/prims/1195142953
http://www.ems-ph.org/doi/10.2977/prims/1195142953
4
Asymptotic Expansion of Singular Solutions and the Characteristic Polygon of Linear Partial Differential Equations in the Complex Domain
Sunao
Ōuchi
Sophia University, TOKYO, JAPAN
Complex partial differential equations, solutions with asymptotic expansion
Let P(z, ∂) be a linear partial differential operator with holomorphic coefficients in a neighborhood Ω of z = 0 in ℂd+1. Consider the equation P(z, ∂)u(z) = f(z), where u(z) admits singularities on the surface K = {z0 = 0} and f(z) has an asymptotic expansion of Gevrey type with respect to z0 as z0 → 0. We study the possibility of asymptotic expansion of u(z). We define the characteristic polygon of P(z, ∂) with respect to K and characteristic indices. We discuss the behavior of u(z) in a neighborhood of K, by using these notions. The main result is a generalization of that in [6].
Partial differential equations
General
457
482
10.2977/prims/1195142869
http://www.ems-ph.org/doi/10.2977/prims/1195142869
Bounds of Operator Functions and Furuta Inequalities
Chia-Shiang
Lin
Bishop’s University, LENNOXVILLE (QUEBEC), CANADA
In this paper we shall find bounds of operator functions of the Furuta types, and bounds of the monotone decreasing function Fp,t(A, B, r, s) of operators in particular. Consequently, we obtain bounds of Furuta inequalities.
Operator theory
General
483
490
10.2977/prims/1195142870
http://www.ems-ph.org/doi/10.2977/prims/1195142870
Invariant Sheaves
Masaki
Kashiwara
Kyoto University, KYOTO, JAPAN
Algebraic geometry
General
491
509
10.2977/prims/1195142871
http://www.ems-ph.org/doi/10.2977/prims/1195142871
The Generalized Fock Implementation of Complex Orthogonal Transformations
Paul Lee
Robinson
University of Florida, GAINESVILLE, UNITED STATES
We determine precise necessary and sufficient conditions for a complex orthogonal transformation to admit a generalized implementing operator in a Fock representation, extending classical results due to Shale–Stinespring and Carey–Palmer.
Linear and multilinear algebra; matrix theory
Quantum theory
General
511
531
10.2977/prims/1195142872
http://www.ems-ph.org/doi/10.2977/prims/1195142872
Zero actions and energy functions for perfect crystals
Timothy
Baker
Kyoto University, KYOTO, JAPAN
We give a combinatorial description of the action of the crystal operators ẽ0, f~0 on certain perfect crystals of U'q(Cn(1)), U'q(Dn(1)) and U'q(Dn+1(2)), by means of Dynkin diagram automorphisms and Schensted column insertion. Also, for certain level 1 perfect crystals of these algebras we give a definition of a combinatorial "charge" related to the energy function on homogeneous paths in such crystals.
Nonassociative rings and algebras
Combinatorics
Quantum theory
General
533
572
10.2977/prims/1195142873
http://www.ems-ph.org/doi/10.2977/prims/1195142873
5
Asymptotic Distribution of Eigenfrequencies for Damped Wave Equations
Johannes
Sjöstrand
Ecole Polytechnique, PALAISEAU CEDEX, FRANCE
Damped wave equations, non-selfadjoint, eigenvalue asymptotics
The eigenfrequencies associated to a damped wave equation, are known to belong to a band parallel to the real axis. We establish Weyl asymptotics for the distribution of the real parts of the eigenfrequencies, we show that up to a set of density 0, the eigenfrequencies are confined to a band determined by the Birkhoff limits of the damping coefficient. We also show that certain averages of the imaginary parts converge to the average of the damping coefficient.
Partial differential equations
General
573
611
10.2977/prims/1195142811
http://www.ems-ph.org/doi/10.2977/prims/1195142811
On the Approximation of Blow-up Time for Solutions of Nonlinear Parabolic Equations
Takeo
Ushijima
Hokkaido University, SAPPORO, JAPAN
There are many nonlinear parabolic equations whose solutions develop singularity in finite time, say T. In many cases, a certain norm of the solution tends to infinity as time t approaches T. Such a phenomenon is called blow-up, and T is called the blow-up time. This paper is concerned with approximation of blow-up phenomena in nonlinear parabolic equations. For numerical computations or for other reasons, we often have to deal with approximate equations. But it is usually not at all clear if such wild phenomena as blow-up can be well reflected in the approximate equations. In this paper we present rather simple but general sufficient conditions which guarantee that the blow-up time for the original equation is well approximated by that for approximate equations. We will then apply our result to various examples.
Numerical analysis
Partial differential equations
General
613
640
10.2977/prims/1195142812
http://www.ems-ph.org/doi/10.2977/prims/1195142812
A Rohlin Property for One-parameter Automorphism Groups of the Hyperfinite II1 Factor
Keiko
Kawamuro
University of Tokyo, TOKYO, JAPAN
We first define a Rohlin property for one-parameter automorphism groups of the hyperfinite type II1 factor as an analogue of Kishimoto's definition for one-parameter automorphism groups of unital simple C*-algebras. Secondly, we prove equivalence between the Rohlin property and the cohomology vanishing in an appropriate central sequence algebra, which is a variation of Kishimoto's theorem in C*-algebra theory.
Functional analysis
General
641
657
10.2977/prims/1195142813
http://www.ems-ph.org/doi/10.2977/prims/1195142813
6
Singularities at Infinity and their Vanishing Cycles, II. Monodromy
Dirk
Siersma
Universiteit Utrecht, UTRECHT, NETHERLANDS
Mihai
Tibăr
Université Lille I, VILLENEUVE D'ASCQ CEDEX, FRANCE
Topology of polynomial functions, singularities at infinity, relative monodromy
Let f : ℂn —> ℂ be any polynomial function. By using global polar methods, we introduce models for the fibers of f and we study the monodromy at atypical values of f, including the value infinity. We construct a geometric monodromy with controlled behavior and define global relative monodromy with respect to a general linear form. We prove localization results for the relative monodromy and derive a zeta-function formula for the monodromy around an atypical value. We compute the relative zeta function in several cases and emphasize the differences to the “classical” local situation.
Several complex variables and analytic spaces
General
659
679
10.2977/prims/1195139641
http://www.ems-ph.org/doi/10.2977/prims/1195139641
Morphisms of Certain Banach C*-Modules
Fabio
Bagarello
Università degli Studi di Palermo, PALERMO, ITALY
Camillo
Trapani
Università degli Studi di Palermo, PALERMO, ITALY
Morphisms and representations of a class of Banach C*-modules, called CQ*-algebras, are considered. Together with a general method for constructing CQ*-algebras, two different ways of extending the GNS-representation are presented.
Functional analysis
General
681
705
10.2977/prims/1195139642
http://www.ems-ph.org/doi/10.2977/prims/1195139642
Hilbert Space Theory for Reflectionless Relativistic Potentials
Simon
Ruijsenaars
Centre for Mathematics and Computer Science, AMSTERDAM, NETHERLANDS
We study Hilbert space aspects of explicit eigenfunctions for analytic difference operators that arise in the context of relativistic two-particle Calogero–Moser systems. We restrict attention to integer coupling constants g/ℏ, for which no reflection occurs. It is proved that the eigenfunction transforms are isometric, provided a certain dimensionless parameter a varies over a bounded interval (0,amax), whereas isometry is shown to be violated for generic a larger than amax. The anomaly is encoded in an explicit finite-rank operator, whose rank increases to ∞ as a goes to ∞.
Quantum theory
Special functions
Operator theory
General
707
753
10.2977/prims/1195139643
http://www.ems-ph.org/doi/10.2977/prims/1195139643