
Commutative Harmonic Analysis III
Generalized Functions. Application
Springer (Publisher)
Published on 21. October 2012
Book
Paperback/Softback
VII, 268 pages
978-3-642-63380-5 (ISBN)
Description
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.
More details
Series
Edition
Softcover reprint of the original 1st ed. 1995
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
VII, 268 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 16 mm
Weight
429 gr
ISBN-13
978-3-642-63380-5 (9783642633805)
DOI
10.1007/978-3-642-57854-0
Schweitzer Classification
Other editions
Additional editions

Book
08/1995
1st Edition
Springer
€101.60
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Persons
Content
I. Distributions and Harmonic Analysis.- II. Optical and Acoustic Fourier Processors.- III. The Uncertainty Principle in Harmonic Analysis.