Concrete Functional Calculus

  • R. M. Dudley
  • R. Norvaiša

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xii
  2. R. M. Dudley, R. Norvaiša
    Pages 1-15
  3. R. M. Dudley, R. Norvaiša
    Pages 103-214
  4. R. M. Dudley, R. Norvaiša
    Pages 215-235
  5. R. M. Dudley, R. Norvaiša
    Pages 237-272
  6. R. M. Dudley, R. Norvaiša
    Pages 273-333
  7. R. M. Dudley, R. Norvaiša
    Pages 335-391
  8. R. M. Dudley, R. Norvaiša
    Pages 393-406
  9. R. M. Dudley, R. Norvaiša
    Pages 407-503
  10. R. M. Dudley, R. Norvaiša
    Pages 505-549
  11. R. M. Dudley, R. Norvaiša
    Pages 551-569
  12. R. M. Dudley, R. Norvaiša
    Pages 571-643
  13. Back Matter
    Pages 645-671

About this book

Introduction

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.

Keywords

Composition operator Integration Interval functions Nemytskii operator Nonlinear integral equations Product integral Riemann-Stieltjes integral p-variation

Authors and affiliations

  • R. M. Dudley
    • 1
  • R. Norvaiša
    • 2
  1. 1.Technology, Department of MathematicsMassachusetts Institute ofCambridgeUSA
  2. 2.Institute of Mathematics and InformaticsVilniusLithuania

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-6950-7
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4419-6949-1
  • Online ISBN 978-1-4419-6950-7
  • Series Print ISSN 1439-7382
  • About this book