Explaining and comparing the various standard types of generalised functions which have been developed during the 20th Century, this text also contains accounts of recent non-standard theories of distributions, ultradistributions and Stato-hyperfunctions. The book could readily be used as a main text on generalised functions for mathematical undergraduates in final year analysis courses, as it presupposes little more than a general mathematical background. It also makes a valuable reference text for non-specific applied mathematics students, such as physicists or electrical engineers, needing to gain expertise in the application of generalised functions to physical problems, without any prior acquaintance of the specialised subject matter. An ideal companion book to Delta Functions, also by Professor Hoskins.
Explains and compares the various standard types of generalised functions that have been developed during the 20th Century
Contains accounts of recent non-standard theories of distributions, ultradistributions and Stato-hyperfunctions
Mathematical undergraduates and non-specific applied mathematics students, such as physicists or electrical engineers
Table of Contents
Introduction to distributions; Further properties of distributions; Generalised functions and fourier analysis; Analytic representation; Multiplication of generalised functions; Infinitesimal analysis; Non-standard theories; References and index.
An original and smart attempt to cover various developments of the theory of generalized and new generalized functions, beginning with the simplest considerations on distributions and finishing with deep remarks on the links with non-standard analysis. As far as I know, this is the only book to achieve this goal. …highly recommendable., Zentralblatt Math