Topological Vector Spaces and Their Applications

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

Auteur

Vladimir Bogachev, born in 1961, Professor at the Department of Mechanics and Mathematics of Lomonosov Moscow State University and at the Faculty of Mathematics of the Higher School of Economics (Moscow, Russia) is an expert in measure theory and infinite-dimensional analysis and the author of more than 200 papers and 12 monographs, including his famous two-volume treatise "Measure theory" (Springer, 2007), "Gaussian measures" (AMS, 1997), "Differentiable measures and the Malliavin calculus" (AMS, 2010), "Fokker-Planck-Kolmogorov equations" (AMS, 2015), and others. An author with a high citation index (h=31 with more than 4700 citations according to the Google Scholar), Vladimir Bogachev solved several long-standing problems in measure theory and Fokker-Planck-Kolmogorov equations.

Oleg Smolyanov, born in 1938, Professor at the Department of Mechanics and Mathematics of Lomonosov Moscow State University is an expert in topological vector spacesand infinite-dimensional analysis and author of more than 200 papers and 5 monographs. Oleg Smolyanov solved several long-standing problems in the theory of topological vector spaces.

Contenu

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.