Siddiqi A.H. Functional Analysis and Applications

Springer Nature Singapore Pte Ltd. 2018. — 594 p. — (Industrial and Applied Mathematics). — ISBN: 9811037248.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.Banach Contraction Fixed Point Theorem
Banach Spaces
Hilbert Spaces
Fundamental Theorems
Differential and Integral Calculus in Banach Spaces
Optimization Problems
Operator Equations and Variational Methods
Finite Element and Boundary Element Methods
Variational Inequalities and Applications
Spectral Theory with Applications
Frame and Basis Theory in Hilbert Spaces
Wavelet Theory
Wavelet Method for Partial Differential Equations and Image Processing
Wavelet Frames
Gabor Analysis