Distribution, Integral Transforms and Applications
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A01=Urszula Sztaba
A01=W. Kierat
advanced distribution theory problems
Author_Urszula Sztaba
Author_W. Kierat
Category=PBKF
Category=PBKJ
cauchy
Cauchy Prob Lem
Cauchy Sequence
Cauchy Transform
Condit Ions
Cont Inui Ty
Continuous Linear Form
Convolution Product
Distr Ibut Ions
Easy Computa
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equali Ty
Fol Lowing
Fol Lowing THEOREM
fourier
Fourier analysis applications
funct
functional analysis
General Izat Ion
H I Lbe R T
Holomorphic Function
Ibut Ions
Lebesgue Dominated Convergence Theorem
Lebesgue integration
Linear Partial Differential Operators
Malgrange-Ehrenpreis theorem
Poisson Summat Ion Formula
product
rem
S Impl
Schwartz kernel theorem
sect
sequence
T Ra
Tempered Dis
tensor
Tensor Product
theo
topological vector spaces
TTX
Unders Tood
verif
Product details
- ISBN 9780367395551
- Weight: 453g
- Dimensions: 178 x 254mm
- Publication Date: 23 Sep 2019
- Publisher: Taylor & Francis Ltd
- Publication City/Country: GB
- Product Form: Paperback
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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.
Kierat, W.; Sztaba, Urszula
