The Moment Problem
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Beschreibung
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.
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
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
Autor*in
Konrad Schmüdgen
Themen in »The Moment Problem«
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
Stimmen zu »The Moment Problem«
“The virtue of Schmüdgen's graduate textbook is that it lays solid foundations for any further explorations, theoretical or applied, in the complex and dynamical realm of moment problems. … This volume will definitely be the reference to moment problems for several future generations.” (Mihai Putinar,Mathematical Reviews, 2018)
“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)
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