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Generalized Functions and Their Applications - R. S. Pathak

Generalized Functions and Their Applications

By: R. S. Pathak (Editor)

Hardcover

Published: 30th April 1993
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The International Symposium on Generalized Functions and Their Applications was organized by the Department of Mathematics, Banaras Hindu University, and held December 23-26, 1991, on the occasion of the Platinum Jubilee Celebration of the university. More than a hundred mathematicians from ten countries participated in the deliberations of the symposium. Thirty lectures were delivered on a variety of topics within the area. The contributions to the proceedings of the symposium are, with a few exceptions, expanded versions of the lectures delivered by the invited speakers. The survey papers by Komatsu and Hoskins and Sousa Pinto provide an up-to-date account of the theory of hyperfunctions, ultradistributions and microfunctions, and the nonstandard theory of new generalized functions, respectively; those by Stankovic and Kanwal deal with structures and asymptotics. Choquet-Bruhat's work studies generalized functions on manifold and gives applications to shocks and discrete models. The other contributions relate to contemporary problems and achievements in theory and applications, especially in the theory of partial differential equations, differential geometry, mechanics, mathematical physics, and systems science. The proceedings give a very clear impression of the present state of the art in this field and contain many challenges, ideas, and open problems. The volume is very helpful for a broad spectrum of readers: graduate students to mathematical researchers.

Reproducing Kernels on the Unit Spherep. 1
Ultradistributional Boundary Values of Holomorphic Functionsp. 11
Cauchy Representation of Distributions and Applications to Probability IIp. 29
Applications of Generalized Functions to Shocks and Discrete Modelsp. 37
Perturbation Expansion for Distributions on Surfaces with Lagrange-Burmann Theorem and Applications to Mechanicsp. 51
Generalized D'Alembert Functional Equation in Distributionsp. 53
Riesz Bases of Special Polynomials in Weighted Sobolev Spaces of Analytic Functionsp. 61
Toeplitz Operators Acting on Generalized Functionsp. 87
Nonstandard Treatments of New Generalized Functionsp. 95
Interplay between Singularities, Asymptotics and Generalized Functionsp. 109
Hyperfunctions, Ultradistributions and Microfunctionsp. 119
Generalized Functions for the Laplace Transform and Universal Approximantsp. 131
An Extension of the Radon Transformp. 141
On the Expansion of Zonal Holomorphic Functions on the Complex Spherep. 149
A Convolution Structure for Almost Invariant Operators on Homogeneous Banach Space of Distributionsp. 157
Characterization of Functions with Fourier Transforms Supported on Orthantsp. 167
Pseudo-Asymptotic Expansion of Generalized Functionsp. 175
Multipliers, Convolutors and Hypoelliptic Convolutors for Tempered Ultradistributionsp. 183
The Hilbert Spaces of Szego Type and Fourier-Laplace Transforms on R[superscript n]p. 197
New Saddle Point Theoremsp. 213
Multiplication and Quasiasymptotic Behaviour in Generalized Fock Spacesp. 221
Some Remarks on the Distributional Hankel Transformp. 235
Applications of Distributions and Currents in Complex Analytic Geometryp. 241
Structural Problems of the Asymptotic Behaviour of Generalized Functionsp. 251
Distributional Form Invariant Linear Systemsp. 265
On Certain Total Biorthogonal Systems in Banach Spacesp. 271
Analytic Representations of Tempered Distributions Using Waveletsp. 281
A Lower Estimate for the Norm of a Pseudodifferential Operator Modulo Compact Operatorsp. 293
Contributorsp. 299
Indexp. 303
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780306444043
ISBN-10: 0306444046
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 308
Published: 30th April 1993
Publisher: Springer Science+Business Media
Country of Publication: US
Dimensions (cm): 23.4 x 15.6  x 1.91
Weight (kg): 1.38