Concrete Functional Calculus

• Main Authors: Dudley, R. M. (Author), Norvaiša, R. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2011.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Functional analysis.; Integral equations.; Operator theory.; Functions of real variables.; Functional Analysis.; Integral Equations.; Operator Theory.; Real Functions.

Concrete Functional Calculus focuses primarily on differentiability of some nonlinear operators on functions or pairs of functions.  This  includes composition of two functions, and the product integral, taking a matrix- or operator-valued coefficient function into a solution of a system of linear d...

Table of Contents:

• Preface
• 1 Introduction and Overview
• 2 Definitions and Basic Properties of Extended Riemann-Stieltjes Integrals
• 3 Phi-variation and p-variation; Inequalities for Integrals
• 4 Banach Algebras
• 5 Derivatives and Analyticity in Normed Spaces
• 6 Nemytskii Operators on Some Function Spaces
• 7 Nemytskii Oerators on Lp Spaces
• 8 Two-Function Composition
• 9 Product Integration
• 10 Nonlinear Differential and Integral Equations
• 11 Fourier Series
• 12 Stochastic Processes and Phi-Variation
• Appendix Nonatomic Measure Spaces
• References
• Subject Index
• Author Index
• Index of Notation.