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Concrete Functional Calculus
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Concrete Functional Calculus

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ISBN-13:
9781441969507
Einband:
eBook
Seiten:
671
Autor:
R. M. Dudley
Serie:
Springer Monographs in Mathematics Schriftenreihe Markt und Marketing
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
Beschreibung:

This book 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.

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.
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.

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