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.
| ISBN: | 9781441969491 |
| Publication date: | 10th November 2010 |
| Author: | R M Dudley, Rimas Norvaisa |
| Publisher: | Springer an imprint of Springer New York |
| Format: | Hardback |
| Pagination: | 671 pages |
| Series: | Springer Monographs in Mathematics |
| Genres: |
Functional analysis and transforms Integral calculus and equations Real analysis, real variables |