Topological Vector Spaces and Their Applications
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Beschreibung
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.
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. Overall, 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.
Offers a concise course on topological vector spaces oriented towards readers interested in infinite-dimensional analysis Introduces a systematic and accessible presentation for beginners of measure theory on infinite-dimensional spaces in its interplay with the theory of topological vector spaces Explores differential calculus on general locally convex spaces Includes supplementary material: sn.pub/extras Includes supplementary material: sn.pub/extras
Autor*in
V.I. Bogachev
Themen in »Topological Vector Spaces and Their Applications«
46A03, 58C20, 28C20 Topological vector space Locally convex space Differentiation in infinite-dimensional spaces Integration in infinite-dimensional spaces Measures on infinite-dimensional spaces
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“The book under review presents an excellent modern treatment of topological linear spaces. Moreover, in contrast to existing monographs on this topic it adds material on applications that are not covered elsewhere. … The book is well written and elucidates basic concepts with a large list of examples.” (Jan Hamhalter, Mathematical Reviews, November, 2017)
“This is indeed a good book, well written, that includes much useful material. The basic theory is presented in a clear, understandable way. Moreover, many recent, important, more specialized results are also included with precise references. This book is recommendable for analysts interested in the modern theory of locally convex spaces and its applications, and especially for those mathematicians who might use differentiation theory on infinite-dimensional spaces or measure theory on topological vector spaces.” (José Bonet, zbMATH 1378.46001, 2018)
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