Overview
- Three levels of exposition in this book oriented towards different categories of readers
- ranging from graduate students and PhD students to professional researchers
- Based on lectures given at Mekhmat (Department of Mechanics and Mathematics of Moscow State University), one of the top mathematical departments worldwide, with its rich traditions of teaching functional analysis
- Extensive additional information is presented in complementary sections and exercises provided with detailed hints or references
Part of the book series: Moscow Lectures (ML, volume 4)
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Table of contents (12 chapters)
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Front Matter
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Back Matter
Keywords
- meromorphic functions
- Riemann theorem
- harmonic functions
- Fuchsian groups
- Riemann surfaces
- moduli of Riemann surfaces
- algebraic curves
- Riemann-Roch theorem
- Weierstrass points
- Abel theorem
- theta function
- Baker-Akhiezer function
- Kadomtsev-Petviashvili (KP) hierarchy
- algebro-geometric solutions of KP
- dispersionless 2D Toda hierarchy
- conformal mappings to disk
About this book
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.
Reviews
Authors and Affiliations
About the authors
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.Bibliographic Information
Book Title: Real and Functional Analysis
Authors: Vladimir I. Bogachev, Oleg G. Smolyanov
Series Title: Moscow Lectures
DOI: https://doi.org/10.1007/978-3-030-38219-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-38218-6Published: 26 February 2020
Softcover ISBN: 978-3-030-38221-6Published: 26 February 2021
eBook ISBN: 978-3-030-38219-3Published: 25 February 2020
Series ISSN: 2522-0314
Series E-ISSN: 2522-0322
Edition Number: 1
Number of Pages: XVI, 586
Additional Information: This book is an expanded and revised version of the work first published in Russian in 2009 (1st edition) and 2011 (2nd edition) with the publisher Regular and Chaotic Dynamics, Moscow - Izhevsk, under the title ?????????????? ? ???????????
Topics: Analysis