The Moment Problem

  • Konrad Schmüdgen

Part of the Graduate Texts in Mathematics book series (GTM, volume 277)

Table of contents

  1. Front Matter
    Pages i-xxiii
  2. Konrad Schmüdgen
    Pages 13-41
  3. Konrad Schmüdgen
    Pages 43-54
  4. The One-Dimensional Moment Problem

    1. Front Matter
      Pages 55-55
    2. Konrad Schmüdgen
      Pages 79-91
    3. Konrad Schmüdgen
      Pages 93-119
    4. Konrad Schmüdgen
      Pages 145-175
  5. The One-Dimensional Truncated Moment Problem

    1. Front Matter
      Pages 201-201
    2. Konrad Schmüdgen
      Pages 257-279
  6. The Multidimensional Moment Problem

    1. Front Matter
      Pages 281-281
    2. Konrad Schmüdgen
      Pages 283-313
    3. Konrad Schmüdgen
      Pages 357-380
    4. Konrad Schmüdgen
      Pages 381-398
  7. The Multidimensional Truncated Moment Problem

  8. Back Matter
    Pages 499-535

About this book


This advanced textbook provides a comprehensive and unified account of the moment problem. It covers the classical one-dimensional theory and its multidimensional generalization, including modern methods and recent developments.

In both the one-dimensional and multidimensional cases, the full and truncated moment problems are carefully treated separately. Fundamental concepts, results and methods are developed in detail and accompanied by numerous examples and exercises. Particular attention is given to powerful modern techniques such as real algebraic geometry and Hilbert space operators. A wide range of important aspects are covered, including the Nevanlinna parametrization for indeterminate moment problems, canonical and principal measures for truncated moment problems, the interplay between Positivstellensätze and moment problems on semi-algebraic sets, the fibre theorem, multidimensional determinacy theory, operator-theoretic approaches, and the existence theory and important special topics of multidimensional truncated moment problems.

The Moment Problem will be particularly useful to graduate students and researchers working on moment problems, functional analysis, complex analysis, harmonic analysis, real algebraic geometry, polynomial optimization, or systems theory. With notes providing useful background information and exercises of varying difficulty illustrating the theory, this book will also serve as a reference on the subject and can be used for self-study.


MSC (2010): 44A60, 14P10, 47A57 Hamburger moment problem Stieltjes moment problem Hausdorff moment problem orthogonal polynomials Jacobi operators Nevanlinna parametrization Weyl circle Carleman condition canonical solutions principal solutions positive polynomials Positivstellensätze moment problem on semi-algebraic sets Polynomial optimization Hankel matrix

Authors and affiliations

  • Konrad Schmüdgen
    • 1
  1. 1.Mathematisches InstitutUniversität LeipzigGermany

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