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Overview"This book is based on lectures given at ""Mekhmat"", the Department of Mechanics and Mathematics at Moscow State University, one of the top mathematical departments worldwide, with a rich tradition of teaching functional analysis. Featuring an advanced course on real and functional analysis, the book presents not only core material traditionally included in university courses of different levels, but also a survey of the most important results of a more subtle nature, which cannot be considered basic but which are useful for applications. Further, it includes several hundred exercises of varying difficulty with tips and references. The book is intended for graduate and PhD students studying real and functional analysis as well as mathematicians and physicists whose research is related to functional analysis. " Full Product DetailsAuthor: Vladimir I. Bogachev , Oleg G. SmolyanovPublisher: Springer Nature Switzerland AG Imprint: Springer Nature Switzerland AG Edition: 1st ed. 2020 Volume: 4 Weight: 1.063kg ISBN: 9783030382186ISBN 10: 3030382184 Pages: 586 Publication Date: 26 February 2020 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Language: English Table of ContentsMetric and Topological Spaces.- Fundamentals of Measure Theory.- The Lebesgue Integral.- Connections between the Integral and Derivative.- Normed and Euclidean Spaces.- Linear Operators and Functionals.- Spectral Theory.- Locally Convex Spaces and Distributions.- The Fourier Transform and Sobolev Spaces.- Unbounded Operators and Operator Semigroups.- Banach Algebras.- Infinite-Dimensional AnalysisReviewsThe book is almost 600 pages long and very comprehensive, with many interesting examples. Its style and notation make it very readable. ... Also, references are given where you can go deeper and deeper into any of them. ... I believe that the book is clear, dense, concise and very well done. The older I get, the more appreciate 'a ready, concise, clear explanation' and I have found the book plenty of them. (Jose Mendoza, zbMATH 1466.26002, 2021) “The book is almost 600 pages long and very comprehensive, with many interesting examples. Its style and notation make it very readable. ... Also, references are given where you can go deeper and deeper into any of them. ... I believe that the book is clear, dense, concise and very well done. The older I get, the more appreciate ‘a ready, concise, clear explanation’ and I have found the book plenty of them.” (José Mendoza, zbMATH 1466.26002, 2021) Author Information"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), ""Topological vector spaces and their applications"" (Springer, 2017), ""Weak convergence of measures"" (AMS, 2018) , and others. An author with a high citation index (h=34 with more than 7000 citations according to the Google Scholar), Vladimir Bogachev solved several long-standing problems in measure theory and Fokker-Planck-Kolmogorov equations. He received Award of the Japan Society for Promotion of Science and Kolmogorov’s Prize of the Russian Academy of Science. Oleg Smolyanov, born in 1938, Professor at the Department of Mechanics and Mathematics of Lomonosov Moscow State University is an expert in topological vector spaces and infinite-dimensional analysis and author of more than 200 papers and 5 monographs (including ""Topological vector spaces and their applications"" (Springer, 2017) coauthored with Vladimir Bogachev). Oleg Smolyanov solved several long-standing problems in the theory of topological vector spaces." Tab Content 6Author Website:Countries AvailableAll regions |
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