Overview
- 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
Part of the book series: Graduate Texts in Mathematics (GTM, volume 277)
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Table of contents (19 chapters)
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Front Matter
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The One-Dimensional Moment Problem
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Front Matter
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The One-Dimensional Truncated Moment Problem
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Front Matter
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Keywords
- 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
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.
Reviews
“The bibliography includes many older and newer titles, the author being one of the main contributors in the last forty years. The book is well-written and it can be considered as an up-to day reference book for the use of both beginners and confirmed researchers, oriented not only to the domain of moment problems but also to other branches of analysis, or of mathematics, in general.” (Florian-Horia Vasilescu, zbMATH, 2018)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: The Moment Problem
Authors: Konrad Schmüdgen
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-3-319-64546-9
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-64545-2Published: 22 November 2017
Softcover ISBN: 978-3-319-87817-1Published: 31 August 2018
eBook ISBN: 978-3-319-64546-9Published: 09 November 2017
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 1
Number of Pages: XXIII, 512
Number of Illustrations: 6 b/w illustrations
Topics: Functional Analysis, Operator Theory, Field Theory and Polynomials, Algebraic Geometry