Commutative Harmonic Analysis III : Generalized Functions. Application

Language: English

Published by Springer Berlin Heidelberg, 2012

3642633803 / 9783642633805

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Druck auf Anfrage Neuware - Printed after ordering - The theory of generalized functions is a general method that makes it possible to consider and compute divergent integrals, sum divergent series, differentiate discontinuous functions, perform the operation of integration to any complex power and carry out other such operations that are impossible in classical analysis. Such operations are widely used in mathematical physics and the theory of differential equations, where the ideas of generalized func tions first arose, in other areas of analysis and beyond. The point of departure for this theory is to regard a function not as a mapping of point sets, but as a linear functional defined on smooth densi ties. This route leads to the loss of the concept of the value of function at a point, and also the possibility of multiplying functions, but it makes it pos sible to perform differentiation an unlimited number of times. The space of generalized functions of finite order is the minimal extension of the space of continuous functions in which coordinate differentiations are defined every where. In this sense the theory of generalized functions is a development of all of classical analysis, in particular harmonic analysis, and is to some extent the perfection of it. The more general theories of ultradistributions or gener alized functions of infinite order make it possible to consider infinite series of generalized derivatives of continuous functions.

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Title
Commutative Harmonic Analysis III : Generalized Functions. Application
Author
V. P. Havin
Publisher
Springer Berlin Heidelberg
Publication year
2012
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
3642633803
ISBN 13
9783642633805
Item weight
429 grams
Dimensions
235x155x16 mm

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