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Author: N.I. Akhiezer
Publisher: SIAM
ISBN: 1611976391
Category : Mathematics
Languages : en
Pages : 267
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Book Description
The mathematical theory for many application areas depends on a deep understanding of the theory of moments. These areas include medical imaging, signal processing, computer visualization, and data science. The problem of moments has also found novel applications to areas such as control theory, image analysis, signal processing, polynomial optimization, and statistical big data. The Classical Moment Problem and Some Related Questions in Analysis presents a unified treatment of the development of the classical moment problem from the late 19th century to the middle of the 20th century. Important connections between the moment problem and many branches of analysis are presented. In this self-contained text, readers will find a unified exposition of important classical results, which are difficult to read in the original journals, as well as a strong foundation for many areas in modern applied mathematics. Researchers in areas that use techniques developed for the classical moment problem will find the book of interest.
Author: N.I. Akhiezer
Publisher: SIAM
ISBN: 1611976391
Category : Mathematics
Languages : en
Pages : 267
Get Book Here
Book Description
The mathematical theory for many application areas depends on a deep understanding of the theory of moments. These areas include medical imaging, signal processing, computer visualization, and data science. The problem of moments has also found novel applications to areas such as control theory, image analysis, signal processing, polynomial optimization, and statistical big data. The Classical Moment Problem and Some Related Questions in Analysis presents a unified treatment of the development of the classical moment problem from the late 19th century to the middle of the 20th century. Important connections between the moment problem and many branches of analysis are presented. In this self-contained text, readers will find a unified exposition of important classical results, which are difficult to read in the original journals, as well as a strong foundation for many areas in modern applied mathematics. Researchers in areas that use techniques developed for the classical moment problem will find the book of interest.
Author: N. I. Akhiezer
Publisher: Courier Dover Publications
ISBN: 0486845559
Category : Mathematics
Languages : en
Pages : 273
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Book Description
This text provides a classic treatment of issues associated with the moment problem that also involve linear algebra, probability theory, stochastic processes, quantum fields, signal processing, and more. 1965 edition.
Author: Mark Grigorʹevich Kreĭn
Publisher: American Mathematical Soc.
ISBN: 9780821886403
Category : Functional analysis
Languages : en
Pages : 282
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Book Description
Author: Naum Ilʹich Akhiezer
Publisher:
ISBN:
Category :
Languages : en
Pages : 253
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Book Description
Author: Mark Grigorʹevich Kreĭn
Publisher: American Mathematical Soc.
ISBN: 9780821886717
Category : Mathematics
Languages : en
Pages : 430
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Book Description
In this book, an extensive circle of questions originating in the classical work of P. L. Chebyshev and A. A. Markov is considered from the more modern point of view. It is shown how results and methods of the generalized moment problem are interlaced with various questions of the geometry of convex bodies, algebra, and function theory. From this standpoint, the structure of convex and conical hulls of curves is studied in detail and isoperimetric inequalities for convex hulls are established; a theory of orthogonal and quasiorthogonal polynomials is constructed; problems on limiting values of integrals and on least deviating functions (in various metrics) are generalized and solved; problems in approximation theory and interpolation and extrapolation in various function classes (analytic, absolutely monotone, almost periodic, etc.) are solved, as well as certain problems in optimal control of linear objects.
Author: Daniel Alpay
Publisher: Springer Science & Business Media
ISBN: 3034804288
Category : Mathematics
Languages : en
Pages : 306
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Book Description
The origins of Schur analysis lie in a 1917 article by Issai Schur in which he constructed a numerical sequence to correspond to a holomorphic contractive function on the unit disk. These sequences are now known as Schur parameter sequences. Schur analysis has grown significantly since its beginnings in the early twentieth century and now encompasses a wide variety of problems related to several classes of holomorphic functions and their matricial generalizations. These problems include interpolation and moment problems as well as Schur parametrization of particular classes of contractive or nonnegative Hermitian block matrices. This book is primarily devoted to topics related to matrix versions of classical interpolation and moment problems. The major themes include Schur analysis of nonnegative Hermitian block Hankel matrices and the construction of Schur-type algorithms. This book also covers a number of recent developments in orthogonal rational matrix functions, matrix-valued Carathéodory functions and maximal weight solutions for particular matricial moment problems on the unit circle.
Author: Fabrizio Colombo
Publisher: Birkhäuser
ISBN: 3319623621
Category : Mathematics
Languages : en
Pages : 398
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Book Description
This book gathers contributions written by Daniel Alpay’s friends and collaborators. Several of the papers were presented at the International Conference on Complex Analysis and Operator Theory held in honor of Professor Alpay’s 60th birthday at Chapman University in November 2016. The main topics covered are complex analysis, operator theory and other areas of mathematics close to Alpay’s primary research interests. The book is recommended for mathematicians from the graduate level on, working in various areas of mathematical analysis, operator theory, infinite dimensional analysis, linear systems, and stochastic processes.
Author: James Alexander Shohat
Publisher: American Mathematical Soc.
ISBN: 0821815016
Category : Mathematics
Languages : en
Pages : 160
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Book Description
The book was first published in 1943 and then was reprinted several times with corrections. It presents the development of the classical problem of moments for the first 50 years, after its introduction by Stieltjes in the 1890s. In addition to initial developments by Stieltjes, Markov, and Chebyshev, later contributions by Hamburger, Nevanlinna, Hausdorff, Stone, and others are discussed. The book also contains some results on the trigonometric moment problem and a chapter devoted to approximate quadrature formulas.
Author: K.D. Bierstedt
Publisher: Elsevier
ISBN: 0080515924
Category : Mathematics
Languages : en
Pages : 469
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Book Description
This Proceedings Volume contains 32 articles on various interesting areas ofpresent-day functional analysis and its applications: Banach spaces andtheir geometry, operator ideals, Banach and operator algebras, operator andspectral theory, Frechet spaces and algebras, function and sequence spaces.The authors have taken much care with their articles and many papers presentimportant results and methods in active fields of research. Several surveytype articles (at the beginning and the end of the book) will be very usefulfor mathematicians who want to learn "what is going on" in some particularfield of research.
Author: Donald G. Babbitt
Publisher: American Mathematical Soc.
ISBN: 9780821896709
Category : Mathematics
Languages : en
Pages : 762
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Book Description
This second volume of Featured Reviews makes available special detailed reviews of some of the most important mathematical articles and books published from 1997 through 1999. Also included are excellent reviews of several classic books and articles published prior to 1970. Among those reviews, for example, are the following: Homological Algebra by Henri Cartan and Samuel Eilenberg, reviewed by G. Hochschild; Faisceaux algebriques coherents by Jean-Pierre Serre, reviewed by C. Chevalley; and On the Theory of General Partial Differential Operators by Lars Hormander, reviewed by J. L. Lions. In particular, those seeking information on current developments outside their own area of expertise will find the volume very useful. By identifying some of the best publications, papers, and books that have had or are expected to have a significant impact in applied and pure mathematics, this volume will serve as a comprehensive guide to important new research across all fields covered by MR.
