Overview
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.
Full Product Details
Author: R. M. Dudley ,
R. Norvaiša
Publisher: Springer-Verlag New York Inc.
Imprint: Springer-Verlag New York Inc.
Edition: 2011 ed.
Volume: 0
Dimensions:
Width: 15.50cm
, Height: 3.60cm
, Length: 23.50cm
Weight: 2.490kg
ISBN: 9781441969491
ISBN 10: 1441969497
Pages: 671
Publication Date: 10 November 2010
Audience:
Professional and scholarly
,
College/higher education
,
Professional & Vocational
,
Postgraduate, Research & Scholarly
Format: Hardback
Publisher's Status: Active
Availability: In Print
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Reviews
From the reviews: 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)
Author Information
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 Norvaisa is a principal researcher at the Institute of Mathematics and Informatics in Lithuania. Dudley and Norvaisa 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"".
