This self-contained textbook discusses all major topics in functional analysis. Combining classical materials with new methods, it supplies numerous relevant solved examples and problems and discusses the applications of functional analysis in diverse fields. The book is unique in its scope, and a variety of applications of functional analysis and operator-theoretic methods are devoted to each area of application. Each chapter includes a set of problems, some of which are routine and elementary, and some of which are more advanced. The book is primarily intended as a textbook for graduate and advanced undergraduate students in applied mathematics and engineering. It offers several attractive features making it ideally suited for courses on functional analysis intended to provide a basic introduction to the subject and the impact of functional analysis on applied and computational mathematics, nonlinear functional analysis and optimization. It introduces emerging topics like wavelets, Gabor system, inverse problems and application to signal and image processing.

Offers a self-contained textbook for a range of courses on functional analysis Provides a clear overview of the basics of functional analysis Supplies numerous relevant solved examples and problems Discusses the applications of functional analysis in diverse fields

Autorentext

YURI A. FARKOV is a distinguished scientist and professor at the Russian Presidential Academy of National Economy and Public Administration (RANEPA), Moscow, Russia. Earlier, he worked as a professor and head of the Department of Mathematics at the Russian State Geological Prospecting University, Moscow, Russia, from 1997 to 2014; a professor and head of the Department of Higher Mathematics at Dubna International University, Dubna, Russia, from 1996 to 2000; an associate professor at the Department of Higher Mathematics and Mathematical Modelling, Moscow State Geological Prospecting Academy, from 1988 to 1997; and a lecturer at the Department of Higher Mathematics, Moscow State University of Mechanical Engineering "Environmental and Chemical Engineering Institute", Moscow, from 1981 to 1988. In 2013, Prof. Farkov received his DSc-Doctor Fiz.- Mat. Nauk from the People's Friendship University of Russia on "Optimal Methods of Approximation of Function by Generalized Polynomials and Wavelets". In 1981, he received his PhD degree in Mathematics from Moscow Region Pedagogical Institute, on topic "Investigations of Asymptotic and Approximation Properties of Faber-Erokhin Basis Functions". From 1977 to 1980, he did his postgraduate studies at the Moscow Electro-Technical Engineering Institute; and in 1975, he received his BSc degree in Mathematics from Uralsk Pedagogical Institute, Kazakhstan. Professor Farkov is on the editorial boards of the journals American Journal of Computational Mathematics, Communications in Mathematics and Applications and International Journal of Education. He is a member of the Moscow Mathematical Society and American Mathematical Society. His research interests include mathematical analysis, wavelet theory, dyadic analysis and approximation theory. PAMMY MANCHANDA is a senior professor of mathematics at Guru Nanak Dev University, Amritsar, India. She has attended and delivered talks and chaired sessions at reputed academic conferences and workshops across the world, including ICIAM (1999-2015) and ICM since 2002. She was invited twice to the Industrial Mathematics Group of Professor Helmut Neunzert, Kaiserslautern University, Germany, and visited the International Centre for Theoretical Physics (a UNESCO institution) at Trieste, Italy, many times to carry out her research activities. She was the joint secretary of the Indian Society of Industrial and Applied Mathematics (ISIAM) from 1999 until 2016 and after that, she is the secretary of the society. She has been actively engaged in organizing international conferences by the society. She is the managing editor of the Indian Journal of Industrial and Applied Mathematics (by ISIAM) and a member of the editorial board of the Springer's book series, Industrial and Applied Mathematics. With a research interest in functional analysis and applications (financial and meteorological data) and wavelet theory, Prof.Manchanda has published 54 research papers in several international journals of repute, edited 3 proceedings of international conferences of ISIAM and co-authored 3 books. ABUL HASAN SIDDIQI is a distinguished scientist and professor emeritus at the School of Basic Sciences and Research at Sharda University, Greater Noida, India. He was also a visiting consultant at the International Centre for Theoretical Physics (ICTP), Trieste, Italy; Sultan Qaboos University, Muscat, Oman; MIMOS, Kuala Lumpur, Malaysia; and professor at several reputed universities including Aligarh Muslim University (Aligarh, India) and King Fahd University of Petroleum & Minerals (Dhahran, Saudi Arabia). He has a long association with ICTP (a UNESCO institution) in several capacities: short-time visitor, long-duration visitor, regular associate, guests of the director and senior associate. He was awarded the German Academic Exchange Fellowship thrice to carry out mathematical research in Germany. He has published more th

Inhalt

Metric Spaces and Banach Fixed Point Theorem.- Banach Spaces.- Hilbert Space.- Fundamental Theorems.- Differential and Integral Calculus in Banach Spaces.- Optimisation Problems.- Operator Equations and Variational Methods.- Finite Element and Boundary Element Methods.- Variational Inequalities and Applications.- Spectral Theory with Application.- Frame and Basis Theory in Hilbert Spaces.- Wavelet Theory.- Wavelet Method for Partial Dierential Equations and Image Processing.- Wavelet Frames.- Gabor Analysis.