Distributions, Ultradistributions and Other Generalized Functions

Hoskins

ISBN 10: 0132179369 ISBN 13: 9780132179362

Casa editrice: Ellis Horwood Ltd, 1994

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This text compares and evaluates various approaches to the theory of distributions which have appeared since the original presentation by Laurent Schwartz in the 1950s. In so doing, it attempts to clarify some of the differences in notation and terminology which have arisen. It includes a systematic treatment of the ultradistributions which arise in connections with the extended definition of the Fourier transform. The authors discuss the problems posed by the definition of "irregular operations" on generalized functions and review solutions proposed by recent researchers. Apart from the introduction of further new classes of generalized functions using standard mathematical methods, the text contains an account of non-standard analysis and its applications to this field.

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