Concrete Functional Calculus (Springer Monographs in Mathematics) - Softcover

Dudley, R. M.; Norvaiša, R.

Softcover

ISBN 10: 1461427401 ISBN 13: 9781461427407

Publisher: Springer, 2012

Synopsis

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. In this book existence and uniqueness of solutions are proved under suitable assumptions for nonlinear integral equations with respect to possibly discontinuous functions having unbounded variation.

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 this title

About the Author

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".

From the Back Cover

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.

Edition details

• Publisher: Springer
• Publication date: 2012
• Language: English
• ISBN 10: 1461427401
• ISBN 13: 9781461427407
• Binding: Paperback
• Number of pages: 683