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. Opens new possibilities to analysis of statistical functionals and gives an alternative (non-Ito) approach to stochastic calculus Contains new material about the existence and smoothnesss of several nonlinear operators acting between spaces of functions having bounded p-variation Will appeal to graduate students and researchers working on variousaspects of calculus of non-smooth functions INDICE: 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. "
- ISBN: 978-1-4419-6949-1
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 672
- Fecha Publicación: 28/12/2010
- Nº Volúmenes: 1
- Idioma: Inglés