Real and Functional Analysis - Smolyanov, Oleg G.

. .

Résumé :
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. ...

Biographie:
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....

Sommaire:
Vladimir Bogachev was born in Moscow in 1961. He got the PhD at Moscow State University in 1986 and he got the degree of Doctor of Sciences in 1990. Since 1986 Vladimir Bogachev has worked at the Department of Mechanics and Mathematics of Moscow State University. The main fields of his research are measure theory, nonlinear functional analysis, probability theory, and stochastic analysis. He is a well-nown expert in measure theory, probability theory, and the Malliavin calculus, and the author of more than 100 scientific publications. His monograph ``Gaussian Measures'' (AMS, 1998) has become a widely used source. Vladimir Bogachev hs been an invited speaker and a lecturer at many international conferences and several dozen universities and mathematical institutes over the world. Scientific awards: a medal of the Academy of Sciences of the USSR and the Award of the Japan Society of Promotion of Science....