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European Mathematical Society Publishing House
2024-03-29 11:03:43
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https://www.ems-ph.org/meta/jmeta-stream.php?jrn=PRIMS&vol=30&iss=2&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
30
1994
2
Solvability of Convolution Operators
Yasunori
Okada
Chiba University, CHIBA, JAPAN
We study the Surjectivity of convolution operators on the spaces of hyperfunctions and Fourier hyperfunctions. On the space of hyperfunctions, we give a sufficient condition (the kernel is a nonzero ultradistribution), weaker than earlier conditions. On the space of Fourier hyperfunction, we give a new sufficient condition and new necessary conditions for the Surjectivity. Especially in one dimensional case, they become a sufficient and necessary condition. To this aim we use the Fourier analysis as in L. Ehrenpreis [E-2] and T. Kawai [Ka-1].
Fourier analysis
General
167
190
10.2977/prims/1195166127
http://www.ems-ph.org/doi/10.2977/prims/1195166127
Representations of Witt Algebras
Senapathi
Rao
Tata Institute of Fundamental Research, BOMBAY, INDIA
In this paper we construct new families of representations for the Lie-algebra of diffeomorphisms of the torus Td and describe its sub representations.
Nonassociative rings and algebras
General
191
201
10.2977/prims/1195166128
http://www.ems-ph.org/doi/10.2977/prims/1195166128
A Characterization for Fourier Hyperfunctions
Jaeyoung
Chung
Kunsan National University, KUNSAN, SOUTH KOREA
Soon-Yeong
Chung
Sogang University, SEOUL, SOUTH KOREA
Dohan
Kim
Seoul National University, SEOUL, SOUTH KOREA
The space of test functions for Fourier hyperfunctions is characterized by two conditions sup |φ (x)| exp k|x|
Functional analysis
General
203
208
10.2977/prims/1195166129
http://www.ems-ph.org/doi/10.2977/prims/1195166129
PBW Basis of Quantized Universal Enveloping Algebras
Yoshihisa
Saito
University of Tokyo, TOKYO, JAPAN
Nonassociative rings and algebras
General
209
232
10.2977/prims/1195166130
http://www.ems-ph.org/doi/10.2977/prims/1195166130
Oriented Z4 Actions without Stationary Points
Tamio
Hara
Tokyo University of Science, CHIBA-KEN, JAPAN
Manifolds and cell complexes
General
233
248
10.2977/prims/1195166131
http://www.ems-ph.org/doi/10.2977/prims/1195166131
Operators Characterized by Certain Cauchy-Schwarz Type Inequalities
Hideharu
Watanabe
Kyushu University, FUKUOKA, JAPAN
A Hilbert space operator T satisfying either (**) |(T ξ, η)|2 ≤ (|T| ξ,ξ) (|T| η,η) for all ξ, η ∈ ℋ, or (*) |(T ξ, ξ)| ≤ (|(T|ξ,ξ) for all ξ ∈ ℋ, is studied. The condition (**) defines a slightly larger class than the hyponormality, and for compact operators (**) is equivalent to the normality. The condition (*) is characterized by using an operator whose numerical radius is less than 1, and among other things we show that (*) and the normality are equivalent for matrices. Moreover, we show that (*) and the normality are equivalent for trace class operators in Appendix.
Operator theory
General
249
259
10.2977/prims/1195166132
http://www.ems-ph.org/doi/10.2977/prims/1195166132
Fibrewise Hopf Construction and Hoo Formula for Pairings
Nobuyuki
Oda
Fukuoka University, FUKUOKA, JAPAN
Let Γ be a fibrewise co-Hopf space over a topological space B. A ΓB-suspension space ΓBX is a generalization of a fibrewise suspension space ΣBX for any fibrewise pointed space X over B. Making use of ΓB-suspension space, we define ΓB-Hopf construction and prove a ΓB-suspension formula which generalizes the suspension formula of C. S. Hoo. The dual formula is also proved.
Algebraic topology
General
261
279
10.2977/prims/1195166133
http://www.ems-ph.org/doi/10.2977/prims/1195166133
Fibrewise Decomposition of Generalized Suspension Spaces and Loop Spaces
Nobuyuki
Oda
Fukuoka University, FUKUOKA, JAPAN
We work in the category TopBB of fibrewise pointed topological spaces over B. Let Γ be a co-Hopf space (which need not be co-associative) in TopBB. The ΓB-suspension space ΓBX and the ΓB-loop space Γ*BX of a fibrewise pointed space X over B are defined as generalization of the usual suspension space ΣX and the loop space ΩX respectively, ΓB-suspension spaces and ΓB-loop spaces have some properties similar to those of the usual suspension spaces and loop spaces. This is an example of Eckmann-Hilton duality. In this paper, decomposition theorems of ΓB-suspension space ΓBX and ΓB-loop space Γ*BX are proved. Short exact sequences of homotopy sets involving ΓB-suspension spaces or ΓB-loop spaces are obtained in the category of algebraic loops.
Algebraic topology
General
281
295
10.2977/prims/1195166134
http://www.ems-ph.org/doi/10.2977/prims/1195166134
A Process Associated with the Radially Symmetric Dirac Equation
Brian
Jefferies
University of New South Wales, SYDNEY, AUSTRALIA
The dynamical group associated with the Dirac equation with a radially symmetric potential is represented in terms of integrals with respect to the operator valued set functions associated with the Dirac equation in four space-time dimensions.
Quantum theory
General
297
325
10.2977/prims/1195166135
http://www.ems-ph.org/doi/10.2977/prims/1195166135
Classical Theta Functions and Quantum Tori
Alan
Weinstein
University of California, BERKELEY, UNITED STATES
The Schwartz kernel of the multiplication operation on a quantum torus is shown to be the distributional boundary value of a classical multivariate theta function. The kernel satisfies a Schrödinger equation in which the role of time is played by the deformation parameter ℏ and the role of the hamiltonian by a Poisson structure. At least in some special cases, the kernel can be written as a sum of products of single variable theta functions.
Quantum theory
General
327
333
10.2977/prims/1195166136
http://www.ems-ph.org/doi/10.2977/prims/1195166136
Indecomposable Restricted Representations of Quantum sl2
Vyjayanthi
Chari
University of California, RIVERSIDE, UNITED STATES
Alexander
Premet
The University of Manchester, MANCHESTER, UNITED KINGDOM
We construct and classify all the indecomposable restricted representations of Uq(sl2 when q is a root of unity.
Nonassociative rings and algebras
General
335
352
10.2977/prims/1195166137
http://www.ems-ph.org/doi/10.2977/prims/1195166137