eBook ISBN:  9780821892527 
Product Code:  PSAPM/37.E 
List Price:  $99.00 
MAA Member Price:  $89.10 
AMS Member Price:  $79.20 
eBook ISBN:  9780821892527 
Product Code:  PSAPM/37.E 
List Price:  $99.00 
MAA Member Price:  $89.10 
AMS Member Price:  $79.20 

Book DetailsProceedings of Symposia in Applied MathematicsVolume: 37; 1987; 154 ppMSC: Primary 44
Function theory, spectral decomposition of operators, probability, approximation, electrical and mechanical inverse problems, prediction of stochastic processes, the design of algorithms for signalprocessing VLSI chips—these are among a host of important theoretical and applied topics illuminated by the classical moment problem. To survey some of these ramifications and the research which derives from them, the AMS sponsored the Short Course Moments in Mathematics at the Joint Mathematics Meetings, held in San Antonio, Texas, in January 1987. This volume contains the six lectures presented during that course. The papers are likely to find a wide audience, for they are expository, but nevertheless lead the reader to topics of current research.
In his paper, Henry J. Landau sketches the main ideas of past work related to the moment problem by such mathematicians as Caratheodory, Herglotz, Schur, Riesz, and Krein and describes the way the moment problem has interconnected so many diverse areas of research. J. H. B. Kemperman examines the moment problem from a geometric viewpoint which involves a certain natural duality method and leads to interesting applications in linear programming, measure theory, and dilations. Donald Sarason first provides a brief review of the theory of unbounded selfadjoint operators then goes on to sketch the operatortheoretic treatment of the Hamburger problem and to discuss Hankel operators, the AdamjanArovKrein approach, and the theory of unitary dilations. Exploring the interplay of trigonometric moment problems and signal processing, Thomas Kailath describes the role of Szegő polynomials in linear predictive coding methods, parallel implementation, onedimensional inverse scattering problems, and the Toeplitz moment matrices. Christian Berg contrasts the multidimensional moment problem with the onedimensional theory and shows how the theory of the moment problem may be viewed as part of harmonic analysis on semigroups.
Starting from a historical survey of the use of moments in probability and statistics, Persi Diaconis illustrates the continuing vitality of these methods in a variety of recent novel problems drawn from such areas as WienerIto integrals, random graphs and matrices, Gibbs ensembles, cumulants and selfsimilar processes, projections of highdimensional data, and empirical estimation.

Table of Contents

Articles

H. J. Landau — Classical background of the moment problem [ MR 921082 ]

J. H. B. Kemperman — Geometry of the moment problem [ MR 921083 ]

Donald Sarason — Moment problems and operators in Hilbert space [ MR 921084 ]

Thomas Kailath — Signal processing applications of some moment problems [ MR 921085 ]

Christian Berg — The multidimensional moment problem and semigroups [ MR 921086 ]

Persi Diaconis — Application of the method of moments in probability and statistics [ MR 921087 ]


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Function theory, spectral decomposition of operators, probability, approximation, electrical and mechanical inverse problems, prediction of stochastic processes, the design of algorithms for signalprocessing VLSI chips—these are among a host of important theoretical and applied topics illuminated by the classical moment problem. To survey some of these ramifications and the research which derives from them, the AMS sponsored the Short Course Moments in Mathematics at the Joint Mathematics Meetings, held in San Antonio, Texas, in January 1987. This volume contains the six lectures presented during that course. The papers are likely to find a wide audience, for they are expository, but nevertheless lead the reader to topics of current research.
In his paper, Henry J. Landau sketches the main ideas of past work related to the moment problem by such mathematicians as Caratheodory, Herglotz, Schur, Riesz, and Krein and describes the way the moment problem has interconnected so many diverse areas of research. J. H. B. Kemperman examines the moment problem from a geometric viewpoint which involves a certain natural duality method and leads to interesting applications in linear programming, measure theory, and dilations. Donald Sarason first provides a brief review of the theory of unbounded selfadjoint operators then goes on to sketch the operatortheoretic treatment of the Hamburger problem and to discuss Hankel operators, the AdamjanArovKrein approach, and the theory of unitary dilations. Exploring the interplay of trigonometric moment problems and signal processing, Thomas Kailath describes the role of Szegő polynomials in linear predictive coding methods, parallel implementation, onedimensional inverse scattering problems, and the Toeplitz moment matrices. Christian Berg contrasts the multidimensional moment problem with the onedimensional theory and shows how the theory of the moment problem may be viewed as part of harmonic analysis on semigroups.
Starting from a historical survey of the use of moments in probability and statistics, Persi Diaconis illustrates the continuing vitality of these methods in a variety of recent novel problems drawn from such areas as WienerIto integrals, random graphs and matrices, Gibbs ensembles, cumulants and selfsimilar processes, projections of highdimensional data, and empirical estimation.

Articles

H. J. Landau — Classical background of the moment problem [ MR 921082 ]

J. H. B. Kemperman — Geometry of the moment problem [ MR 921083 ]

Donald Sarason — Moment problems and operators in Hilbert space [ MR 921084 ]

Thomas Kailath — Signal processing applications of some moment problems [ MR 921085 ]

Christian Berg — The multidimensional moment problem and semigroups [ MR 921086 ]

Persi Diaconis — Application of the method of moments in probability and statistics [ MR 921087 ]