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＜電子ブック＞
Concrete Functional Calculus / by R. M. Dudley, R. Norvaiša
(Springer Monographs in Mathematics. ISSN:21969922)

版	1st ed. 2011.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2011
本文言語	英語
大きさ	XII, 671 p : online resource
著者標目	*Dudley, R. M author Norvaiša, R author SpringerLink (Online service)
件　名	LCSH:Functional analysis LCSH:Integral equations LCSH:Operator theory LCSH:Functions of real variables FREE:Functional Analysis FREE:Integral Equations FREE:Operator Theory FREE:Real Functions
一般注記	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 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.  For nonlinear integral equations with respect to possibly discontinuous functions having unbounded variation, existence and uniqueness of solutions are proved under suitable assumptions. Key features and topics: * Extensive usage of p-variation of functions * 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 HTTP:URL=https://doi.org/10.1007/978-1-4419-6950-7

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