Marat V. Markin Elementary Functional Analysis Also of Interest Real Analysis. Measure and Integration Marat V. Markin, 2019 ISBN 978-3-11-060097-1, e-ISBN (PDF) 978-3-11-060099-5, e-ISBN (EPUB) 978-3-11-059882-7 Elementary Operator Theory Marat V. Markin, 2019 ISBN 978-3-11-060096-4, e-ISBN (PDF) 978-3-11-060098-8, e-ISBN (EPUB) 978-3-11-059888-9 Applied Nonlinear Functional Analysis. An Introduction Nikolaos S. Papageorgiou, Patrick Winkert, 2018 ISBN 978-3-11-051622-7, e-ISBN (PDF) 978-3-11-053298-2, e-ISBN (EPUB) 978-3-11-053183-1 Functional Analysis. A Terse Introduction Gerardo Chacón, Humberto Rafeiro, Juan Camilo Vallejo, 2017 ISBN 978-3-11-044191-8, e-ISBN (PDF) 978-3-11-044192-5, e-ISBN (EPUB) 978-3-11-043364-7 Complex Analysis. A Functional Analytic Approach Friedrich Haslinger, 2017 ISBN 978-3-11-041723-4, e-ISBN (PDF) 978-3-11-041724-1, e-ISBN (EPUB) 978-3-11-042615-1 Marat V. Markin Elementary Functional Analysis | Mathematics Subject Classification 2010 46-02, 47-02, 46A22, 46A30, 46A32, 46A35, 46A45, 46B03, 46B04, 46B10, 46C05, 47A30 Author Prof. Dr. Marat V. Markin California State University, Fresno Department of Mathematics 5245 North Backer Avenue, M/S PB 108 Fresno, CA 93740 USA
[email protected] ISBN 978-3-11-061391-9 e-ISBN (PDF) 978-3-11-061403-9 e-ISBN (EPUB) 978-3-11-061409-1 Library of Congress Control Number: 2018950580 Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.dnb.de. © 2018 Walter de Gruyter GmbH, Berlin/Boston Cover image: Mordolff / Getty Images Typesetting: VTeX UAB, Lithuania Printing and binding: CPI books Lecks, GmbH www.degruyter.com | To my students, past, present, and future. Preface Functional analysis arose in the early twentieth century and gradually, conquering one stronghold after another, became a nearly universal mathematical doctrine, not merely a new area of mathematics, but a new mathematical world view. Its appearance was the inevitable consequence of the evolution of all of nineteenth-century mathematics, in particular classical analysis and mathematical physics. Its original basis was formed by Cantor’s theory of sets and linear algebra. Its existence answered the question of how to state general principles of a broadly interpreted analysis in a way suitable for the most diverse situations. A. M. Vershik Having at once abandoned futile attempts to say anything better to describe the essence and origins of functional analysis than the above epigraph, the author, echoing [32], could not but choose it as a foreword for this book. And yet, a few more words are to be uttered. Functional analysis The emergence of functional analysis, a vast and rapidly growing branch of modern mathematics using “the intuition and language of geometry in the study of functions” [54], was brought to life by the inherent to mathematics epistemological tendency towards unification and abstraction. The constantly widening field of applications of functional analysis encompasses ordinary and partial differential equations, numerical analysis, calculus of variations, approximation theory, integral equations, and much more. The profoundly abstract nature and extensive applicability of functional analysis make a course in it to be an indispensable part of a contemporary graduate mathematics curriculum increasing its value not only for graduate students majoring in mathematics, but also for those majoring in physics, science, and engineering. The purpose of the book and targeted audience