Springer Monographs in Mathematics

Concrete Functional Calculus

Authors: Dudley, R. M., Norvaiša, R.

  • 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 various aspects of calculus of non-smooth functions
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eBook $159.00
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  • ISBN 978-1-4419-6950-7
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Hardcover $209.00
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  • ISBN 978-1-4419-6949-1
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  • Usually dispatched within 3 to 5 business days.
Softcover $209.00
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  • ISBN 978-1-4614-2740-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

About the authors

Richard M. Dudley is a professor of mathematics at MIT. He has published over a hundred papers in peer-reviewed journals and two books. He was one of three lecturers in the 1982 St.-Flour Summer School in Probability, published in Springer's Lecture Notes in Mathematics series in 1984.

Rimas Norvaiša is a principal researcher at the Institute of Mathematics and Informatics in Lithuania. Dudley and Norvaiša have written one previous book together in 1999 for Springer's Lecture Notes in Mathematics series, entitled "Differentiability of Six Operators on Nonsmooth Functions and P-Variation".

Reviews

From the reviews:

“This monograph is a thorough and masterful work on non-linear analysis designed to be read and studied by graduate students and professional mathematical researchers. The overall perspective and choice of material is highly novel and original. … It is a unique account of some key areas of modern analysis which will surely turn out to be invaluable for many researchers in this and related areas.” (David Applebaum, The Mathematical Gazette, Vol. 98 (541), March, 2014)

“The present monograph is quite extensive and interesting. It is divided into twelve chapters on different topics on Functional calculus and an appendix on non-atomic measure spaces. … The book has many historical comments and remarks which clarify the developments of the theory. It has also an extensive bibliography with 258 references. … will be very useful for all interested readers in Real-Functional Analysis and Probability.” (Francisco L. Hernandez, The European Mathematical Society, January, 2012)

“The monograph under review aims at analyzing properties such as Hölder continuity, differentiability and analyticity of various types of nonlinear operators which arises in the study of differential and integral equations and in applications to problems of statistics and probability. … this is an interesting book which contains a lot of material.” (Massimo Lanza de Cristoforis, Mathematical Reviews, Issue 2012 e)


Table of contents (12 chapters)

  • Introduction and Overview

    Dudley, R. M. (et al.)

    Pages 1-15

  • Definitions and Basic Properties of Extended Riemann–Stieltjes Integrals

    Dudley, R. M. (et al.)

    Pages 17-102

  • Ф-variation and p-variation; Inequalities for Integrals

    Dudley, R. M. (et al.)

    Pages 103-214

  • Banach Algebras

    Dudley, R. M. (et al.)

    Pages 215-235

  • Derivatives and Analyticity in Normed Spaces

    Dudley, R. M. (et al.)

    Pages 237-272

Buy this book

eBook $159.00
price for USA (gross)
  • ISBN 978-1-4419-6950-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $209.00
price for USA
  • ISBN 978-1-4419-6949-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $209.00
price for USA
  • ISBN 978-1-4614-2740-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Concrete Functional Calculus
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2011
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-1-4419-6950-7
DOI
10.1007/978-1-4419-6950-7
Hardcover ISBN
978-1-4419-6949-1
Softcover ISBN
978-1-4614-2740-7
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XII, 671
Topics