Commutative Harmonic Analysis III
Generalized Functions. Application
Series: Encyclopaedia of Mathematical Sciences; 72;
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Product details:
- Edition number Softcover reprint of the original 1st ed. 1995
- Publisher Springer Berlin Heidelberg
- Date of Publication 21 October 2012
- Number of Volumes 1 pieces, Book
- ISBN 9783642633805
- Binding Paperback
- No. of pages268 pages
- Size 235x155 mm
- Weight 433 g
- Language English
- Illustrations VII, 268 p. Illustrations, black & white 0
Categories
Long 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. This book covers three important topics in commutative harmonic analysis which is a branch of mathematics which has strong links with theoretical physics and signal processing. Hence, it addresses mathematicians, physicists and engineers working in these areas. The group of authors is outstanding.
MoreTable of Contents:
I. Distributions and Harmonic Analysis.- II. Optical and Acoustic Fourier Processors.- III. The Uncertainty Principle in Harmonic Analysis.
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