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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.
This book is an approachable introduction to the theory of distributions and integral transforms. The principle intention of the book is to emphasize the remarkable connections of distribution theory with the classical analysis and the theory of differential equations. First of all it covers the theory of the Lebesque integral as a fundamental tool in the proofs of many theorems. The theory develops from its beginning to the point where many fundamental theorems are proved. It gives practical hints on using the theory of distributions in cases where classical analysis is insufficient. The seven chapters of the book naturally connect general theory, examples and applications and the authors attempt to answer natural questions related to topics presented in the text.
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Nadine Gordimer
Paperback
(2)
R398
R330
Discovery Miles 3 300
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