Generalized Functions and Their Applications

ISBN-13: 9780306444043 / Angielski / Twarda / 1993 / 308 str.

R. S. Pathak; R. S. Pathak

Opis

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.

Spis treści

Reproducing Kernels on the Unit Sphere (F. Brackx et al.). Ultradistributional Boundary Values of Holomorphic Functions (R.D. Carmichael et al.). Cauchy Representation of Distributions and Applications to Probability II (M.A. Chaudry). Applications of Generalized Functions to Shocks and Discrete Models (Y. ChoquetBruhat). Generalized D'Alembert Functional Equation in Distributions (E.Y. Deeba, E.L. Koh). Riesz Bases of Special Polynomials in Weighted SobolevSpaces of Analytic Functions (J. de Graaf). Toeplitz Operators Acting on Generalized Distributions (M. Hasumi). Nonstandard Treatments of New Generalized Functions (R.F. Hoskins, J. Sousa Pinto). Interplay between Singularities, Asymptotics, and Generalized Functions (R.P. Kanwal). Hyperfunctions, Ultradistributions, and Microfunctions (H. Komatsu). Generalized Functions for the Laplace Transform and Universal Approximants (J.B. Miller). 17 additional articles. Index.