Author : Mark Grigorʹevich Kreĭn
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 50,94 MB
Release : 1968
Category : Functional analysis
ISBN : 9780821886403
Author : N.I. Akhiezer
Publisher : SIAM
Page : 267 pages
File Size : 21,21 MB
Release : 2020-12-01
Category : Mathematics
ISBN : 1611976383
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. Ahiezer
Publisher :
Page : 265 pages
File Size : 49,70 MB
Release : 1985
Category :
ISBN :
Author : Mihály Bakonyi
Publisher : Princeton University Press
Page : 533 pages
File Size : 45,78 MB
Release : 2011-07-18
Category : Mathematics
ISBN : 1400840597
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.
Author : Shozo Koshi
Publisher : World Scientific
Page : 282 pages
File Size : 12,88 MB
Release : 1991-10-31
Category :
ISBN : 9814555924
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.
Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 982 pages
File Size : 23,11 MB
Release : 1994-02-28
Category : Mathematics
ISBN : 9781556080104
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.
Author : Konrad Schmüdgen
Publisher : Springer
Page : 530 pages
File Size : 48,4 MB
Release : 2017-11-09
Category : Mathematics
ISBN : 3319645463
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.
Author : I. M. Glazman
Publisher : Courier Corporation
Page : 548 pages
File Size : 20,81 MB
Release : 2006-01-01
Category : Mathematics
ISBN : 0486453324
A sequence of 2,400 propositions and problems features only hints. Suitable for advanced undergraduates and graduate students, this unique approach encourages students to work out their own proofs. 1974 edition.
Author : Ismail Chamseddine
Publisher : Author House
Page : 154 pages
File Size : 32,13 MB
Release : 2013-05-24
Category : Mathematics
ISBN : 1481796712
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
Author : Raúl E. Curto
Publisher : American Mathematical Soc.
Page : 69 pages
File Size : 36,73 MB
Release : 1996
Category : Mathematics
ISBN : 0821804855
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.
