- ホーム
- > 洋書
- > 英文書
- > Science / Mathematics
Full Description
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.
Contents
Reproducing Kernels on the Unit Sphere.- Ultradistributional Boundary Values of Holomorphic Functions.- Cauchy Representation of Distributions and Applications to Probability II.- Applications of Generalized Functions to Shocks and Discrete Models.- Perturbation Expansion for Distributions on Surfaces with Lagrange-Bürmann Theorem and Applications to Mechanics.- Generalized D'Alembert Functional Equation in Distributions.- Riesz Bases of Special Polynomials in Weighted Sobolev Spaces of Analytic Functions.- Toeplitz Operators Acting on Generalized Functions.- Nonstandard Treatments of New Generalized Functions.- Interplay between Singularities, Asymptotics and Generalized Functions.- Hyperfunctions, Ultradistributions and Microfunctions.- Generalized Functions for the Laplace Transform and Universal Approximants.- An Extension of the Radon Transform.- On the Expansion of Zonal Holomorphic Functions on the Complex Sphere.- A Convolution Structure for Almost Invariant Operators on Homogeneous Banach Space of Distributions.- Characterization of Functions with Fourier Transforms Supported on Orthants.- Pseudo-Asymptotic Expansion of Generalized Functions.- Multipliers, Convolutors and Hypoelliptic Convolutors for Tempered Ultradistributions.- The Hilbert Spaces of Szegö Type and Fourier-Laplace Transforms on ?n.- New Saddle Point Theorems.- Multiplication and Quasiasymptotic Behaviour in Generalized Fock Spaces.- Some Remarks on the Distributional Hankel Transform.- Applications of Distributions and Currents in Complex Analytic Geometry.- Structural Problems of the Asymptotic Behaviour of Generalized Functions.- Distributional Form Invariant Linear Systems.- On Certain Total Biorthogonal Systems in Banach Spaces.- Analytic Representations of Tempered DistributionsUsing Wavelets.- A Lower Estimate for the Norm of a Pseudodifferential Operator Modulo Compact Operators.- Contributors.
