Topological Vector Spaces and Their Applications / by V.I. Bogachev, O.G. Smolyanov.

Format:

Book

Author/Creator:

Bogachev, V.I., Author.

Smolyanov, O.G., Author.

Series:

Springer Monographs in Mathematics, 2196-9922

Language:

English

Subjects (All):

Functional analysis.

Global analysis (Mathematics).

Manifolds (Mathematics).

Measure theory.

Probabilities.

Functional Analysis.

Global Analysis and Analysis on Manifolds.

Measure and Integration.

Probability Theory.

Local Subjects:

Functional Analysis.

Global Analysis and Analysis on Manifolds.

Measure and Integration.

Probability Theory.

Physical Description:

1 online resource (X, 456 p.)

Edition:

1st ed. 2017.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2017.

Summary:

This book gives a compact exposition of the fundamentals of the theory of locally convex topological vector spaces. Furthermore it contains a survey of the most important results of a more subtle nature, which cannot be regarded as basic, but knowledge which is useful for understanding applications. Finally, the book explores some of such applications connected with differential calculus and measure theory in infinite-dimensional spaces. These applications are a central aspect of the book, which is why it is different from the wide range of existing texts on topological vector spaces. In addition, this book develops differential and integral calculus on infinite-dimensional locally convex spaces by using methods and techniques of the theory of locally convex spaces. The target readership includes mathematicians and physicists whose research is related to infinite-dimensional analysis.

Contents:

1. Introduction to the theory of topological vector spaces

2. Methods of constructing topological vector spaces

3. Duality

4. Differential calculus

5.Measures on linear spaces.

Notes:

Includes bibliographical references and indexes.

ISBN:

3-319-57117-6