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Books > Science & Mathematics > Mathematics > Algebra
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The Moment Problem (Paperback, Softcover reprint of the original 1st ed. 2017)
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The Moment Problem (Paperback, Softcover reprint of the original 1st ed. 2017)
Series: Graduate Texts in Mathematics, 277
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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 Positivstellensatze 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.
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