Tauberian Theorems for Generalized Functions / Edition 1

by V.S. Vladimirov, Yu.N. Drozzinov, O.I. Zavialov

Overview

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. The Scandal of Father G. K. Chesterton. 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non­ trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Product Details

ISBN-13:	9789027723833
Publisher:	Springer Netherlands
Publication date:	04/30/1988
Series:	Mathematics and its Applications , #10
Edition description:	1988
Pages:	293
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

Notation and Definitions.- 1: Some Facts on the Theory of Distributions.- 1. Distributions and their properties.- 2. Integral transformations of distributions.- 3. Quasi-asymptotics of distributions.- 2: Many-Dimensional Tauberian Theorems.- 4. The General Tauberian theorem and its consequences.- 5. Admissible and strictly admissible functions.- 6. Comparison Tauberian theorems.- 3: One-Dimensional Tauberian Theorems.- 7. The general Tauberian theorem and its consequences.- 8. Quasi-asymptotic properties of distributions at the origin.- 9. Asymptotic properties of the Fourier transform of distributions from M+.- 10. Quasi-asymptotic expansions.- 4: Asymptotic Properties of Solutions of Convolutions Equations.- 11. Quasi-asymptotics of the fundamental solutions of convolution equations.- 12. Quasi-asymptotics of passive operators.- 5: Tauberian Theorems for Causal Functions.- 13. The Jost-Lehmann-Dyson representation.- 14. Automodel asymptotics for the causal functions and singularities of their Fourier transforms on the light cone.