
Distribution, Integral Transforms and Applications
CRC Press
1st Edition
Published on 23. September 2019
Book
Paperback/Softback
158 pages
978-0-367-39555-1 (ISBN)
Description
The theory of distributions is most often presented as L. Schwartz originally presented it: as a theory of the duality of topological vector spaces. Although this is a sound approach, it can be difficult, demanding deep prior knowledge of functional analysis. The more elementary treatments that are available often consider distributions as limits of sequences of functions, but these usually present the theoretical foundations in a form too simplified for practical applications.
Distributions, Integral Transforms and Applications offers an approachable introduction to the theory of distributions and integral transforms that uses Schwartz's description of distributions as linear continous forms on topological vector spaces. The authors use the theory of the Lebesgue integral as a fundamental tool in the proofs of many theorems and develop the theory from its beginnings to the point of proving many of the deep, important theorems, such as the Schwartz kernel theorem and the Malgrange-Ehrenpreis theorem. They clearly demonstrate how the theory of distributions can be used in cases such as Fourier analysis, when the methods of classical analysis are insufficient.
Accessible to anyone who has completed a course in advanced calculus, this treatment emphasizes the remarkable connections between distributional theory, classical analysis, and the theory of differential equations and leads directly to applications in various branches of mathematics.
Distributions, Integral Transforms and Applications offers an approachable introduction to the theory of distributions and integral transforms that uses Schwartz's description of distributions as linear continous forms on topological vector spaces. The authors use the theory of the Lebesgue integral as a fundamental tool in the proofs of many theorems and develop the theory from its beginnings to the point of proving many of the deep, important theorems, such as the Schwartz kernel theorem and the Malgrange-Ehrenpreis theorem. They clearly demonstrate how the theory of distributions can be used in cases such as Fourier analysis, when the methods of classical analysis are insufficient.
Accessible to anyone who has completed a course in advanced calculus, this treatment emphasizes the remarkable connections between distributional theory, classical analysis, and the theory of differential equations and leads directly to applications in various branches of mathematics.
More details
Series
Language
English
Place of publication
London
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
College/higher education
Dimensions
Height: 254 mm
Width: 178 mm
Thickness: 9 mm
Weight
315 gr
ISBN-13
978-0-367-39555-1 (9780367395551)
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Schweitzer Classification
Other editions
Additional editions

W. Kierat | Urszula Sztaba
Distribution, Integral Transforms and Applications
Book
01/2003
1st Edition
CRC Press
€184.60
Shipment within 15-20 days

W. Kierat | Urszula Sztaba
Distribution, Integral Transforms and Applications
E-Book
01/2003
CRC Press
€89.99
Available for download

W. Kierat | Urszula Sztaba
Distribution, Integral Transforms and Applications
E-Book
01/2003
1st Edition
CRC Press
€89.99
Available for download
Persons
Kierat, W.; Sztaba, Urszula
Content
Definitions and Preliminaries. Local Properties of Distribution. Tensor Products and Convolution Products. Differential Equations. Particular Types of Distribution and Cauchy Transforms. Tempered Distributions and Fourier Transforms. Orthogonal Expansions of Distribution. Appendix: Sequential Completeness of some Spaces.
OTI #1: 2876
OTI #1: 2876