Concrete functional calculus
Author(s)
Bibliographic Information
Concrete functional calculus
（Springer monographs in mathematics）
Springer, c2011
Available at / 20 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Note
Includes bibliographical references (p. [649]-660) and index
Description and Table of Contents
Description
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 differential equations with the given coefficients. In this book existence and uniqueness of solutions are proved under suitable assumptions for nonlinear integral equations with respect to possibly discontinuous functions having unbounded variation. Key features and topics: Extensive usage of p-variation of functions, and applications to stochastic processes.
This work will serve as a thorough reference on its main topics for researchers and graduate students with a background in real analysis and, for Chapter 12, in probability.
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 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.
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