Some Questions In The Theory Of Moments
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Some Questions In The Theory Of Moments
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Author : Mark Grigorʹevich Kreĭn
language : en
Publisher: American Mathematical Soc.
Release Date : 1968
Some Questions In The Theory Of Moments written by Mark Grigorʹevich Kreĭn and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Functional analysis categories.
Some Questions In The Theory Of Moments
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Author : Naum Ilʹich Akhiezer
language : en
Publisher:
Release Date : 1962
Some Questions In The Theory Of Moments written by Naum Ilʹich Akhiezer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962 with Functional analysis categories.
The Classical Moment Problem And Some Related Questions In Analysis
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Author : N.I. Akhiezer
language : en
Publisher: SIAM
Release Date : 2020-12-01
The Classical Moment Problem And Some Related Questions In Analysis written by N.I. Akhiezer and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-01 with Mathematics categories.
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.
Matrix Completions Moments And Sums Of Hermitian Squares
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Author : Mihály Bakonyi
language : en
Publisher: Princeton University Press
Release Date : 2011-07-18
Matrix Completions Moments And Sums Of Hermitian Squares written by Mihály Bakonyi and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-18 with Mathematics categories.
Intensive research in matrix completions, moments, and sums of Hermitian squares has yielded a multitude of results in recent decades. This book provides a comprehensive account of this quickly developing area of mathematics and applications and gives complete proofs of many recently solved problems. With MATLAB codes and more than 200 exercises, the book is ideal for a special topics course for graduate or advanced undergraduate students in mathematics or engineering, and will also be a valuable resource for researchers. Often driven by questions from signal processing, control theory, and quantum information, the subject of this book has inspired mathematicians from many subdisciplines, including linear algebra, operator theory, measure theory, and complex function theory. In turn, the applications are being pursued by researchers in areas such as electrical engineering, computer science, and physics. The book is self-contained, has many examples, and for the most part requires only a basic background in undergraduate mathematics, primarily linear algebra and some complex analysis. The book also includes an extensive discussion of the literature, with close to 600 references from books and journals from a wide variety of disciplines.
Construction Of Random Signals From Their Higher Order Moments
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Author : Ismail Chamseddine
language : en
Publisher: Author House
Release Date : 2013-05-24
Construction Of Random Signals From Their Higher Order Moments written by Ismail Chamseddine and has been published by Author House this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-24 with Mathematics categories.
The book treats the problem of constructing a probability density from moments, comparing with other approaches, like the empirical distribution function. The argumentation is based on deeper considerations of complexity and duality, and proposes the problem as model for concept formation in the human mind. www.momentproblem.blogspot.com
The Moment Problem
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Author : Konrad Schmüdgen
language : en
Publisher: Springer
Release Date : 2017-11-09
The Moment Problem written by Konrad Schmüdgen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-09 with Mathematics categories.
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.
Solution Of The Truncated Complex Moment Problem For Flat Data
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Author : Raúl E. Curto
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Solution Of The Truncated Complex Moment Problem For Flat Data written by Raúl E. Curto and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
We introduce a matricial approach to the truncated complex moment problem, and apply it to the case of moment matrices of flat data type, for which the columns corresponding to the homogeneous monomials in [italic]z and [italic]z̄ of highest degree can be written in terms of monomials of lower degree. We discuss the connection between complex moment problems and the subnormal completion problem for 2-variable weighted shifts, and present in detail the construction of solutions for truncated complex moment problems associated with monomials of degrees one and two.
Encyclopaedia Of Mathematics Set
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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-02-28
Encyclopaedia Of Mathematics Set written by Michiel Hazewinkel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-02-28 with Mathematics categories.
The Encyclopaedia of Mathematics is the most up-to-date, authoritative and comprehensive English-language work of reference in mathematics which exists today. With over 7,000 articles from `A-integral' to `Zygmund Class of Functions', supplemented with a wealth of complementary information, and an index volume providing thorough cross-referencing of entries of related interest, the Encyclopaedia of Mathematics offers an immediate source of reference to mathematical definitions, concepts, explanations, surveys, examples, terminology and methods. The depth and breadth of content and the straightforward, careful presentation of the information, with the emphasis on accessibility, makes the Encyclopaedia of Mathematics an immensely useful tool for all mathematicians and other scientists who use, or are confronted by, mathematics in their work. The Enclyclopaedia of Mathematics provides, without doubt, a reference source of mathematical knowledge which is unsurpassed in value and usefulness. It can be highly recommended for use in libraries of universities, research institutes, colleges and even schools.
Functional Analysis And Related Topics Proceedings Of The International Symposium
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Author : Shozo Koshi
language : en
Publisher: World Scientific
Release Date : 1991-10-31
Functional Analysis And Related Topics Proceedings Of The International Symposium written by Shozo Koshi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-10-31 with categories.
The objective of this symposium is to discuss the recent developments in the various areas of functional analysis. This volume consists mainly of articles in the fields of topological algebra, Banach spaces, function spaces, harmonic analysis, operator theory and application of functional analysis.
Flat Extensions Of Positive Moment Matrices Recursively Generated Relations
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Author : Raúl E. Curto
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Flat Extensions Of Positive Moment Matrices Recursively Generated Relations written by Raúl E. Curto and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
In this book, the authors develop new computational tests for existence and uniqueness of representing measures $\mu$ in the Truncated Complex Moment Problem: $\gamma {ij}=\int \bar zizj\, d\mu$ $(0\le i+j\le 2n)$. Conditions for the existence of finitely atomic representing measures are expressed in terms of positivity and extension properties of the moment matrix $M(n)(\gamma )$ associated with $\gamma \equiv \gamma {(2n)}$: $\gamma {00}, \dots ,\gamma {0,2n},\dots ,\gamma {2n,0}$, $\gamma {00}>0$. This study includes new conditions for flat (i.e., rank-preserving) extensions $M(n+1)$ of $M(n)\ge 0$; each such extension corresponds to a distinct rank $M(n)$-atomic representing measure, and each such measure is minimal among representing measures in terms of the cardinality of its support. For a natural class of moment matrices satisfying the tests of recursive generation, recursive consistency, and normal consistency, the existence problem for minimal representing measures is reduced to the solubility of small systems of multivariable algebraic equations. In a variety of applications, including cases of the quartic moment problem ($n=2$), the text includes explicit contructions of minimal representing measures via the theory of flat extensions. Additional computational texts are used to prove non-existence of representing measures or the non-existence of minimal representing measures. These tests are used to illustrate, in very concrete terms, new phenomena, associated with higher-dimensional moment problems that do not appear in the classical one-dimensional moment problem.