The Bellman Function Technique in Harmonic Analysis
Published on 6. August 2020
Book
Hardback
460 pages
978-1-108-48689-7 (ISBN)
Description
The Bellman function, a powerful tool originating in control theory, can be used successfully in a large class of difficult harmonic analysis problems and has produced some notable results over the last thirty years. This book by two leading experts is the first devoted to the Bellman function method and its applications to various topics in probability and harmonic analysis. Beginning with basic concepts, the theory is introduced step-by-step starting with many examples of gradually increasing sophistication, culminating with Calderon-Zygmund operators and end-point estimates. All necessary techniques are explained in generality, making this book accessible to readers without specialized training in non-linear PDEs or stochastic optimal control. Graduate students and researchers in harmonic analysis, PDEs, functional analysis, and probability will find this to be an incisive reference, and can use it as the basis of a graduate course.
Reviews / Votes
'I first encountered Bellman functions about 35 years ago when advising engineers striving to minimize the expenditure of diamond chips in silicon grinding. Fifteen years later I was amused to learn that Nazarov, Treil, and Volberg successfully applied similar ideas to a variety of problems in harmonic analysis. Together with Vasyunin (and other analysts), they developed these techniques into a powerful tool which is carefully explained in the present book. The book is written on a level accessible to graduate students and I recommend it to everyone who wishes to join the Bellman functions club.' Mikhail Sodin, Tel Aviv UniversityMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
College/higher education
Professional and scholarly
Illustrations
Worked examples or Exercises
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 32 mm
Weight
899 gr
ISBN-13
978-1-108-48689-7 (9781108486897)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Vasily Vasyunin | Alexander Volberg
The Bellman Function Technique in Harmonic Analysis
E-Book
07/2020
Cambridge University Press
€65.99
Available for download
Persons
Vasily Vasyunin is a Leading Researcher at the St Petersburg Department of the Steklov Mathematical Institute of Russian Academy of Sciences and Professor of Saint-Petersburg State University. His research interests include linear and complex analysis, operator models, and harmonic analysis. Vasyunin has taught at universities in Europe, and the United States. He has authored or co-authored over sixty articles.
Content
Introduction; 1. Examples of Bellman functions; 2. What you always wanted to know about Stochastic Optimal Control, but were afraid to ask; 3. Conformal martingales models. Stochastic and classical Ahlfors-Beurling operators; 4. Dyadic models. Application of Bellman technique to upper estimates of singular integrals; 5. Application of Bellman technique to the end-point estimates of singular integrals.