Real and Functional Analysis

Metric 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 Analysis

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.

"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)