Applied Functional Analysis: Numerical Methods, Wavelet Methods, and Image Processing (Chapman & Hall/CRC Pure and Applied Mathematics Book 258)

Guide covers the most current analytical and numerical methods in infinite-dimensional spaces, introducing recent results in wavelet analysis as applied in partial differential equations and signal and image processing. For researchers and practitioners. Includes index and references. The methods of functional analysis have helped solve diverse real-world problems in optimization, modeling, analysis, numerical approximation, and computer simulation. Applied Functional Analysis presents functional analysis results surfacing repeatedly in scientific and technological applications and presides over the most current analytical and numerical methods in infinite-dimensional spaces. This reference highlights critical studies in projection theorem, Riesz representation theorem, and properties of operators in Hilbert space and covers special classes of optimization problems. Supported by 2200 display equations, this guide incorporates hundreds of up-to-date citations. This text deals with basic definitions and examples related to Banach spaces and operators defined on such spaces. It introduces Hilbert space and infinite-dimensional analogue of Euclidean space of finite dimension The main objective of this chapter is to present the Banach contraction fixed point theorem and its applications to the existence of solutions of matrix, integral and differential equations.