00000cmm a22000004a 4500 UP-99796217611212208 Buklod 20250130103455.0 m go j cr ||u|||auu|a 250130s20102011nyu do j eng 9781441969507 (Ebook) 1441969500 (eBook) (iLib)UPD-00214608393 DLC DMLR rda eng DMLUC QA 303 D83 2011 Concrete Functional Calculus [electronic resource] R. M. Dudley, R. Norvaisa. New York, New York Springer New York 2010. ©2011. 1 online resource (xii, 671 pages) illustrations. text rdacontent computer rdamedia online resource rdacarrier Springer monographs in mathematics. 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 probabilit Electronic reproduction. New York SpringerLink 2011. Available via World Wide Web through SpringerLink. Calculus. Functional analysis. Dudley, R. M. (Richard M.) editor. SpringerLink (Online service). Electronic Resource Available for UP System via Springer Link. https://doi.org/10.1007/978-1-4419-6950-7 FO UPD DMLR QA 303 D83 2011 Electronic Resource