Extensions Of Positive Definite Functions

Author : Palle Jorgensen,Steen Pedersen,Feng Tian
Publisher : Springer
Page : 231 pages
File Size : 41,9 Mb
Release : 2016-07-08
Category : Mathematics
ISBN : 9783319397801

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Extensions of Positive Definite Functions by Palle Jorgensen,Steen Pedersen,Feng Tian Pdf

This monograph deals with the mathematics of extending given partial data-sets obtained from experiments; Experimentalists frequently gather spectral data when the observed data is limited, e.g., by the precision of instruments; or by other limiting external factors. Here the limited information is a restriction, and the extensions take the form of full positive definite function on some prescribed group. It is therefore both an art and a science to produce solid conclusions from restricted or limited data. While the theory of is important in many areas of pure and applied mathematics, it is difficult for students and for the novice to the field, to find accessible presentations which cover all relevant points of view, as well as stressing common ideas and interconnections. We have aimed at filling this gap, and we have stressed hands-on-examples.

Author : John R. McMullen
Publisher : American Mathematical Soc.
Page : 71 pages
File Size : 44,7 Mb
Release : 1972
Category : Mathematics
ISBN : 9780821818176

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Extensions of Positive-Definite Functions by John R. McMullen Pdf

Author : Jean-Pierre Gabardo
Publisher : American Mathematical Soc.
Page : 94 pages
File Size : 53,9 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821825518

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Extension of Positive-Definite Distributions and Maximum Entropy by Jean-Pierre Gabardo Pdf

In this work, the maximum entropy method is used to solve the extension problem associated with a positive-definite function, or distribution, defined on an interval of the real line. Garbardo computes explicitly the entropy maximizers corresponding to various logarithmic integrals depending on a complex parameter and investigates the relation to the problem of uniqueness of the extension. These results are based on a generalization, in both the discrete and continuous cases, of Burg's maximum entropy theorem.

Author : Helge Glöckner
Publisher : American Mathematical Soc.
Page : 150 pages
File Size : 55,9 Mb
Release : 2003
Category : Convex bodies
ISBN : 9780821832561

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Positive Definite Functions on Infinite-Dimensional Convex Cones by Helge Glöckner Pdf

A memoir that studies positive definite functions on convex subsets of finite- or infinite-dimensional vector spaces. It studies representations of convex cones by positive operators on Hilbert spaces. It also studies the interplay between positive definite functions and representations of convex cones.

Author : V.P. Havin,N.K. Nikolski
Publisher : Springer Science & Business Media
Page : 335 pages
File Size : 50,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642589461

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Commutative Harmonic Analysis II by V.P. Havin,N.K. Nikolski Pdf

Classical harmonic analysis is an important part of modern physics and mathematics, comparable in its significance with calculus. Created in the 18th and 19th centuries as a distinct mathematical discipline it continued to develop, conquering new unexpected areas and producing impressive applications to a multitude of problems. It is widely understood that the explanation of this miraculous power stems from group theoretic ideas underlying practically everything in harmonic analysis. This book is an unusual combination of the general and abstract group theoretic approach with a wealth of very concrete topics attractive to everybody interested in mathematics. Mathematical literature on harmonic analysis abounds in books of more or less abstract or concrete kind, but the lucky combination as in this volume can hardly be found.

Author : Joseph A. Ball,Yuli Eidelman,J. William Helton,Vadim Olshevsky,James Rovnyak
Publisher : Springer Science & Business Media
Page : 340 pages
File Size : 53,7 Mb
Release : 2007-12-22
Category : Mathematics
ISBN : 9783764385392

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Recent Advances in Matrix and Operator Theory by Joseph A. Ball,Yuli Eidelman,J. William Helton,Vadim Olshevsky,James Rovnyak Pdf

This volume comprises the proceedings of the International Workshop on Operator Theory and Its Applications held at the University of Connecticut in July 2005.

Author : Zoltán Sasvári
Publisher : Wiley-VCH
Page : 216 pages
File Size : 45,8 Mb
Release : 1994-03-18
Category : Mathematics
ISBN : UOM:39015032145206

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Positive Definite and Definitizable Functions by Zoltán Sasvári Pdf

Author : L. Rodman,Ilya M. Spitkovskiĭ,Hugo Jan Woerdeman
Publisher : American Mathematical Soc.
Page : 71 pages
File Size : 42,7 Mb
Release : 2002
Category : Mathematics
ISBN : 9780821829967

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Abstract Band Method via Factorization, Positive and Band Extensions of Multivariable Almost Periodic Matrix Functions, and Spectral Estimation by L. Rodman,Ilya M. Spitkovskiĭ,Hugo Jan Woerdeman Pdf

New versions are developed of an abstract scheme, which are designed to provide a framework for solving a variety of extension problems. The abstract scheme is commonly known as the band method. The main feature of the new versions is that they express directly the conditions for existence of positive band extensions in terms of abstract factorizations (with certain additional properties). The results allow us to prove, among other things, that the band extension is continuous in an appropriate sense. Using the new versions of the abstract band method, we solve the positive extension problem for almost periodic matrix functions of several real variables with Fourier coefficients indexed in a given additive subgroup of the space of variables.This generality allows us to treat simultaneously many particular cases, for example the case of functions periodic in some variables and almost periodic in others. Necessary and sufficient conditions are given for the existence of positive extensions in terms of Toeplitz operators on Besikovitch spaces. Furthermore, when a solution exists a special extension (the band extension) is constructed which enjoys a maximum entropy property.A linear fractional parameterization of the set of all extensions is also provided. We interpret the obtained results (in the periodic case) in terms of existence of a multivariate autoregressive moving averages (ARMA) process with given autocorrelation coefficients, and identify its maximal prediction error. Another application concerns the solution of the positive extension problem in the context of Wiener algebra of infinite operator matrices. It includes the identification of the maximum entropy extension and a description of all positive extensions via a linear fractional formula. In the periodic case it solves a linear estimation problem for cyclostationary stochastic processes.

Author : Palle E.T. Jorgensen
Publisher : American Mathematical Soc.
Page : 266 pages
File Size : 45,8 Mb
Release : 2018-10-30
Category : Harmonic analysis
ISBN : 9781470448806

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Harmonic Analysis: Smooth and Non-smooth by Palle E.T. Jorgensen Pdf

There is a recent and increasing interest in harmonic analysis of non-smooth geometries. Real-world examples where these types of geometry appear include large computer networks, relationships in datasets, and fractal structures such as those found in crystalline substances, light scattering, and other natural phenomena where dynamical systems are present. Notions of harmonic analysis focus on transforms and expansions and involve dual variables. In this book on smooth and non-smooth harmonic analysis, the notion of dual variables will be adapted to fractals. In addition to harmonic analysis via Fourier duality, the author also covers multiresolution wavelet approaches as well as a third tool, namely, L2 spaces derived from appropriate Gaussian processes. The book is based on a series of ten lectures delivered in June 2018 at a CBMS conference held at Iowa State University.

Author : Michael Ruzhansky,Hemen Dutta,Ravi P. Agarwal
Publisher : John Wiley & Sons
Page : 764 pages
File Size : 41,9 Mb
Release : 2018-05-11
Category : Mathematics
ISBN : 9781119414346

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Mathematical Analysis and Applications by Michael Ruzhansky,Hemen Dutta,Ravi P. Agarwal Pdf

An authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications: Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors—a noted team of international researchers in the field— highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications: Selected Topics includes the most recent research from a range of mathematical fields.

Author : Kelly McKennon
Publisher : American Mathematical Soc.
Page : 75 pages
File Size : 51,8 Mb
Release : 1971
Category : Algebraic functions
ISBN : 9780821818114

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Multipliers, Positive Functionals, Positive-Definite Functions, and Fourier-Stieltjes Transforms by Kelly McKennon Pdf

Author : Béla Sz Nagy,Ciprian Foias,Hari Bercovici,László Kérchy
Publisher : Springer Science & Business Media
Page : 481 pages
File Size : 54,5 Mb
Release : 2010-09-01
Category : Mathematics
ISBN : 9781441960931

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Harmonic Analysis of Operators on Hilbert Space by Béla Sz Nagy,Ciprian Foias,Hari Bercovici,László Kérchy Pdf

The existence of unitary dilations makes it possible to study arbitrary contractions on a Hilbert space using the tools of harmonic analysis. The first edition of this book was an account of the progress done in this direction in 1950-70. Since then, this work has influenced many other areas of mathematics, most notably interpolation theory and control theory. This second edition, in addition to revising and amending the original text, focuses on further developments of the theory, including the study of two operator classes: operators whose powers do not converge strongly to zero, and operators whose functional calculus (as introduced in Chapter III) is not injective. For both of these classes, a wealth of material on structure, classification and invariant subspaces is included in Chapters IX and X. Several chapters conclude with a sketch of other developments related with (and developing) the material of the first edition.

Author : I͡Uriĭ Makarovich Berezanskiĭ
Publisher : American Mathematical Soc.
Page : 824 pages
File Size : 51,9 Mb
Release : 1968
Category : Boundary value problems
ISBN : 0821886495

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Expansions in Eigenfunctions of Selfadjoint Operators by I͡Uriĭ Makarovich Berezanskiĭ Pdf

Author : Gregory E. Fasshauer
Publisher : World Scientific
Page : 520 pages
File Size : 52,7 Mb
Release : 2007
Category : Technology & Engineering
ISBN : 9789812706331

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Meshfree Approximation Methods with MATLAB by Gregory E. Fasshauer Pdf

Meshfree approximation methods are a relatively new area of research. This book provides the salient theoretical results needed for a basic understanding of meshfree approximation methods. It places emphasis on a hands-on approach that includes MATLAB routines for all basic operations.

Author : Jens G. Christensen,Susanna Dann,Azita Mayeli,Gestur Ólafsson
Publisher : American Mathematical Soc.
Page : 209 pages
File Size : 52,9 Mb
Release : 2015-10-27
Category : Harmonic analysis
ISBN : 9781470418793

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Trends in Harmonic Analysis and Its Applications by Jens G. Christensen,Susanna Dann,Azita Mayeli,Gestur Ólafsson Pdf

This volume contains the proceedings of the AMS Special Session on Harmonic Analysis and Its Applications held March 29-30, 2014, at the University of Maryland, Baltimore County, Baltimore, MD. It provides an in depth look at the many directions taken by experts in Harmonic Analysis and related areas. The papers cover topics such as frame theory, Gabor analysis, interpolation and Besov spaces on compact manifolds, Cuntz-Krieger algebras, reproducing kernel spaces, solenoids, hypergeometric shift operators and analysis on infinite dimensional groups. Expositions are by leading researchers in the field, both young and established. The papers consist of new results or new approaches to solutions, and at the same time provide an introduction into the respective subjects.