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  3. The Bellman Function Technique in Harmonic Analysis
  • Cited by 12
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    • Publisher:
      Cambridge University Press
      Publication date:
      16 July 2020
      06 August 2020
      ISBN:
      9781108764469
      9781108486897
      DOI:
      https://doi.org/10.1017/9781108764469
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.77kg, 460 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Abstract Analysis, Probability Theory and Stochastic Processes, Statistics and Probability
      Series:
      Cambridge Studies in Advanced Mathematics (186)
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    Subjects:
    Mathematics (general), Mathematics, Abstract Analysis, Probability Theory and Stochastic Processes, Statistics and Probability
    Series:
    Cambridge Studies in Advanced Mathematics (186)
    Information

    Book 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 Calderón–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

    '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 University

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