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European Mathematical Society Publishing House
2024-03-28 17:07:18
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https://www.ems-ph.org/meta/jmeta-stream.php?jrn=PRIMS&vol=40&iss=2&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
40
2004
2
On Theorems of Hardy, Gelfand–Shilov and Beurling for Semisimple Groups
Sundaram
Thangavelu
Indian Institute of Science, BANGALORE, INDIA
Semisimple Lie groups, representations, Fourier transform, heat kernel, entire functions, symmetric spaces, Jacobi transform
In this paper we prove a strong version of Hardy’s theorem for the group Fourier transform on semisimple Lie groups which characterises the Fourier transforms of all functions satisfying Hardy type conditions. In the particular case of SL(2, ℝ) we characterise all such functions and conjecture that the same is true for all rank one semisimple groups. We also establish an analogue of a theorem of Gelfand and Shilov in the context of semisimple groups. A version of Beurling’s theorem which assumes a Cowling–Price condition on the function is also proved. We show that these results yield most of the earlier results as corollaries.
Topological groups, Lie groups
General
311
344
10.2977/prims/1145475806
http://www.ems-ph.org/doi/10.2977/prims/1145475806
On the Stokes Equation with the Leak and Slip Boundary Conditions of Friction Type: Regularity of Solutions
Norikazu
Saito
The University of Tokyo, TOKYO, JAPAN
Regularity, variational inequality, Stokes equation, nonlinear boundary condition
We consider the Stokes equations under some nonlinear boundary conditions, which are described in terms of subdifferentials of maximal monotone graphs and are called leak and slip boundary conditions of friction type. The main objective is to show the existence of strong solutions, say u ∈ H2 and p ∈ H1, to these problems. We start with weak solutions to variational inequalities, and then study the regularity of weak solutions. Our main theorems imply the maximality of Stokes operators with such nonlinear boundary conditions in a suitable Hilbert space and they are of use in analysis of time-dependent problems. Linear boundary conditions of Neumann type, such as slip and penetration conditions, are also discussed.
Partial differential equations
General
345
383
10.2977/prims/1145475807
http://www.ems-ph.org/doi/10.2977/prims/1145475807
Sample Path Large Deviations for Diffusion Processes on Configuration Spaces over a Riemannian Manifold
Michael
Röckner
Universität Bielefeld, BIELEFELD, GERMANY
Tusheng
Zhang
University of Manchester, MANCHESTER, UNITED KINGDOM
Dirichlet forms, intrinsic metric, large deviations, configuration spaces, energy of path, Girsanov transform
In this paper, we establish a sample path large deviation principle for a class of diffusion processes on configuration spaces over a Riemannian manifold. The rate functional turns out to be the energy of the paths associated to the L2-Wasserstein distance.
Probability theory and stochastic processes
Potential theory
General
385
427
10.2977/prims/1145475808
http://www.ems-ph.org/doi/10.2977/prims/1145475808
Decomposition Problem on Endomorphisms of Projective Varieties
Yoshio
Fujimoto
Gifu University, GIFU, JAPAN
Endomorphisms, extremal rays, hyperbolic manifolds, rationally connected varieties
Let Z := X × Y be a product variety of nonsingular projective varieties X and Y. Suppose that KY is not nef but KX is nef. The aim of this note is to study decomposition problems on an endomorphism f : Z → Z of Z.
Algebraic geometry
Several complex variables and analytic spaces
General
429
440
10.2977/prims/1145475809
http://www.ems-ph.org/doi/10.2977/prims/1145475809
A Serre-type Theorem for the Elliptic Lie Algebras with Rank ≥ 2
Hiroyuki
Yamane
Osaka University Graduate School of Science, OSAKA, JAPAN
In 2000, K. Saito and D. Yoshii gave a Serre-type theorem for the simply-laced elliptic Lie algebras. We extend the theorem to that for the elliptic Lie algebras associated with the (reduced marked) elliptic root systems with rank ≥ 2.
Nonassociative rings and algebras
Topological groups, Lie groups
General
441
469
10.2977/prims/1145475810
http://www.ems-ph.org/doi/10.2977/prims/1145475810
Poles and α-points of Meromorphic Solutions of the First Painlevé Hierarchy
Shun
Shimomura
Keio University, YOKOHAMA, JAPAN
The first Painlevé hierarchy, which is a sequence of higher order analogues of the first Painlevé equation, follows from the singular manifold equations for the mKdV hierarchy. For meromorphic solutions of the first Painlevé hierarchy, we give a lower estimate for the number of poles; which is regarded as an extension of one corresponding to the first Painlevé equation, and which indicates a conjecture on the growth order. From our main result, two corollaries follow: one is the transcendency of meromorphic solutions, and the other is a lower estimate for the frequency of α-points. An essential part of our proof is estimation of certain sums concerning the poles of each meromorphic solution.
Ordinary differential equations
Functions of a complex variable
General
471
485
10.2977/prims/1145475811
http://www.ems-ph.org/doi/10.2977/prims/1145475811
A BPE Model for the Burgers Equation
Shigeyoshi
Ogawa
Ritsumeikan University, SHIGA, JAPAN
Arturo
Kohatsu-Higa
Pompeu Fabra University, BARCELONA, SPAIN
We study the BPE (Brownian particle equation) model of the Burgers equation presented in the preceding article [6]. More precisely, we are interested in establishing the existence and uniqueness properties of solutions using probabilistic techniques.
Probability theory and stochastic processes
General
487
505
10.2977/prims/1145475812
http://www.ems-ph.org/doi/10.2977/prims/1145475812
The Equivariant Toda Lattice
Ezra
Getzler
Northwestern University, EVANSTON, UNITED STATES
Dynamical systems and ergodic theory
Differential geometry
General
507
536
10.2977/prims/1145475813
http://www.ems-ph.org/doi/10.2977/prims/1145475813
Relations for Multiple Zeta Values and Mellin Transforms of Multiple Polylogarithms
Jun-ichi
Okuda
Waseda University, TOKYO, JAPAN
Kimio
Ueno
Waseda University, TOKYO, JAPAN
In this paper a relationship between the Ohno relation for multiple zeta values and multiple polylogarithms are discussed. First we introduce generating functions for the Ohno relation, and investigate their properties. We show that there exists a subfamily of the Ohno relation which recovers algebraically its totality. This is proved through analysis of Mellin transform of multiple polylogarithms. Furthermore, this subfamily is shown to be converted to the Landen connection formula for multiple polylogarithms by inverse Mellin transform.
Number theory
Associative rings and algebras
Sequences, series, summability
General
537
564
10.2977/prims/1145475814
http://www.ems-ph.org/doi/10.2977/prims/1145475814
Distributions of Exponential Growth with Support in a Proper Convex Cone
Masanori
Suwa
Sophia University, TOKYO, JAPAN
Distributions of exponential growth, Paley–Wiener theorem, Laplace transform
In this paper we will characterize the spaces of distributions of exponential growth with support in a proper convex cone by the heat kernel method. As application we can obtain the Paley–Wiener theorem for distributions of exponential growth supported by a proper convex cone and Edge-of-the-Wedge theorem for the space of the image by the Fourier–Laplace transform of them.
Functional analysis
Integral transforms, operational calculus
General
565
603
10.2977/prims/1145475815
http://www.ems-ph.org/doi/10.2977/prims/1145475815