Graduate Texts in Mathematics

The Moment Problem

Authors: Schmüdgen, Konrad

  • First book to present a complete and unified treatment of all parts of the classical real moment problem (full and truncated, one-dimensional and multidimensional)
  • Develops classical and recent results with full proofs
  • Contains new results and concepts on the truncated multidimensional moment problem
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Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-319-64546-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for USA
  • ISBN 978-3-319-64545-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

About the authors

​Konrad Schmüdgen is professor at the University of Leipzig, Germany. He discovered the strict Positivstellensatz and developed in this manner the interplay between real algebraic geometry and moment problems. He obtained a number of fundamental results on full and truncated multidimensional moment problems.

Table of contents (19 chapters)

  • Integral Representations of Linear Functionals

    Schmüdgen, Konrad

    Pages 13-41

  • Moment Problems on Abelian ∗-Semigroups

    Schmüdgen, Konrad

    Pages 43-54

  • One-Dimensional Moment Problems on Intervals: Existence

    Schmüdgen, Konrad

    Pages 57-77

  • One-Dimensional Moment Problems: Determinacy

    Schmüdgen, Konrad

    Pages 79-91

  • Orthogonal Polynomials and Jacobi Operators

    Schmüdgen, Konrad

    Pages 93-119

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-319-64546-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for USA
  • ISBN 978-3-319-64545-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Moment Problem
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
277
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-64546-9
DOI
10.1007/978-3-319-64546-9
Hardcover ISBN
978-3-319-64545-2
Series ISSN
0072-5285
Edition Number
1
Number of Pages
XXIII, 512
Number of Illustrations and Tables
6 b/w illustrations
Topics