# Topological Vector Spaces and Their Applications [electronic resource] / by V.I. Bogachev, O.G. Smolyanov.

##### By: Bogachev, V.I [author.].

##### Contributor(s): Smolyanov, O.G [author.] | SpringerLink (Online service).

Material type: TextSeries: Springer Monographs in Mathematics: Publisher: Cham : Springer International Publishing : Imprint: Springer, 2017Description: X, 456 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783319571171.Subject(s): Functional analysis | Global analysis | Mathematics | Distribution (Probability theory | Functional Analysis | Global Analysis and Analysis on Manifolds | Measure and Integration | Probability Theory and Stochastic ProcessesAdditional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 515.7 Online resources: Click here to access online1. 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.

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.

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