Markov operators, positive semigroups, and approximation processes / Francesco Altomare [and three others].

Format:

Book

Author/Creator:

Altomare, Francesco, Author.

Altomare, Francesco, 1951- author.

Series:

De Gruyter studies in mathematics ; Volume 61.

De Gruyter Studies in Mathematics, 0179-0986 ; Volume 61

Language:

English

Subjects (All):

Boundary value problems.

Differential operators.

Semigroups.

Markov operators.

Physical Description:

1 online resource (326 p.)

Edition:

1st ed.

Place of Publication:

Berlin, Germany : De Gruyter, 2014.

Language Note:

English

Summary:

This research monograph gives a detailed account of a theory which is mainly concerned with certain classes of degenerate differential operators, Markov semigroups and approximation processes. These mathematical objects are generated by arbitrary Markov operators acting on spaces of continuous functions defined on compact convex sets; the study of the interrelations between them constitutes one of the distinguishing features of the book. Among other things, this theory provides useful tools for studying large classes of initial-boundary value evolution problems, the main aim being to obtain a constructive approximation to the associated positive C0-semigroups by means of iterates of suitable positive approximating operators. As a consequence, a qualitative analysis of the solutions to the evolution problems can be efficiently developed. The book is mainly addressed to research mathematicians interested in modern approximation theory by positive linear operators and/or in the theory of positive C0-semigroups of operators and evolution equations. It could also serve as a textbook for a graduate level course.

Contents:

Front matter

Preface

Contents

Introduction

Guide to the reader and interdependence of sections

Notation

1. Positive linear operators and approximation problems

2. C0-semigroups of operators and linear evolution equations

3. Bernstein-Schnabl operators associated with Markov operators

4. Differential operators and Markov semigroups associated with Markov operators

5. Perturbed differential operators and modified Bernstein-Schnabl operators

Appendices

Bibliography

Symbol index

Index

Notes:

Description based upon print version of record.

Includes bibliographical references and indexes.

Description based on print version record.

ISBN:

9783110366976

3110366975

9783110386417

3110386410

OCLC:

922637618