Entropy And Multivariable Interpolation

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Entropy and Multivariable Interpolation

Author : Gelu Popescu
Publisher : American Mathematical Soc.
ISBN 13 : 0821839128
Total Pages : 98 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Entropy and Multivariable Interpolation by : Gelu Popescu

Download or read book Entropy and Multivariable Interpolation written by Gelu Popescu and published by American Mathematical Soc.. This book was released on 2006 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: We define a new notion of entropy for operators on Fock spaces and positive multi-Toeplitz kernels on free semigroups. This is studied in connection with factorization theorems for (e.g., multi-Toeplitz, multi-analytic, etc.) operators on Fock spaces. These results lead to entropy inequalities and entropy formulas for positive multi-Toeplitz kernels on free semigroups (resp. multi-analytic operators) and consequences concerning the extreme points of the unit ball of the noncommutative analytic Toeplitz algebra $F ninfty$. We obtain several geometric characterizations of the central intertwining lifting, a maximal principle, and a permanence principle for the noncommutative commutant lifting theorem. Under certain natural conditions, we find explicit forms for the maximal entropy solution of this multivariable commutant lifting theorem. All these results are used to solve maximal entropy interpolation problems in several variables. We obtain explicit forms for the maximal entropy solution (as well as its entropy) of the Sarason, Caratheodory-Schur, and Nevanlinna-Pick type interpolation problems for the noncommutative (resp. commutative) analytic Toeplitz algebra $F ninfty$ (resp. $W ninfty$) and their tensor products with $B({\mathcal H , {\mathcal K )$. In particular, we provide explicit forms for the maximal entropy solutions of several interpolation problems on the unit ball of $\mathbb{C n$.

Maximum Entropy Principle and the Lagrange Interpolation Polynomials

Author : P. Zeephongsekul
Publisher :
ISBN 13 : 9780864441256
Total Pages : 10 pages
Book Rating : 4.4/5 (412 download)

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Book Synopsis Maximum Entropy Principle and the Lagrange Interpolation Polynomials by : P. Zeephongsekul

Download or read book Maximum Entropy Principle and the Lagrange Interpolation Polynomials written by P. Zeephongsekul and published by . This book was released on 1987 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Multivariate Birkhoff Interpolation

Author : Rudolph A. Lorentz
Publisher : Springer
ISBN 13 : 3540473009
Total Pages : 200 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Multivariate Birkhoff Interpolation by : Rudolph A. Lorentz

Download or read book Multivariate Birkhoff Interpolation written by Rudolph A. Lorentz and published by Springer. This book was released on 2006-11-15 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this book is Lagrange, Hermite and Birkhoff (lacunary Hermite) interpolation by multivariate algebraic polynomials. It unifies and extends a new algorithmic approach to this subject which was introduced and developed by G.G. Lorentz and the author. One particularly interesting feature of this algorithmic approach is that it obviates the necessity of finding a formula for the Vandermonde determinant of a multivariate interpolation in order to determine its regularity (which formulas are practically unknown anyways) by determining the regularity through simple geometric manipulations in the Euclidean space. Although interpolation is a classical problem, it is surprising how little is known about its basic properties in the multivariate case. The book therefore starts by exploring its fundamental properties and its limitations. The main part of the book is devoted to a complete and detailed elaboration of the new technique. A chapter with an extensive selection of finite elements follows as well as a chapter with formulas for Vandermonde determinants. Finally, the technique is applied to non-standard interpolations. The book is principally oriented to specialists in the field. However, since all the proofs are presented in full detail and since examples are profuse, a wider audience with a basic knowledge of analysis and linear algebra will draw profit from it. Indeed, the fundamental nature of multivariate nature of multivariate interpolation is reflected by the fact that readers coming from the disparate fields of algebraic geometry (singularities of surfaces), of finite elements and of CAGD will also all find useful information here.

Bernoulli Free-Boundary Problems

Author : Eugene Shargorodsky
Publisher : American Mathematical Soc.
ISBN 13 : 0821841890
Total Pages : 86 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Bernoulli Free-Boundary Problems by : Eugene Shargorodsky

Download or read book Bernoulli Free-Boundary Problems written by Eugene Shargorodsky and published by American Mathematical Soc.. This book was released on 2008 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: Questions of existence, multiplicity, and regularity of free boundaries for prescribed data need to be addressed and their solutions lead to nonlinear problems. In this paper an equivalence is established between Bernoulli free-boundary problems and a class of equations for real-valued functions of one real variable.

Representations of Shifted Yangians and Finite $W$-algebras

Author : Jonathan Brundan
Publisher : American Mathematical Soc.
ISBN 13 : 0821842161
Total Pages : 122 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Representations of Shifted Yangians and Finite $W$-algebras by : Jonathan Brundan

Download or read book Representations of Shifted Yangians and Finite $W$-algebras written by Jonathan Brundan and published by American Mathematical Soc.. This book was released on 2008 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study highest weight representations of shifted Yangians over an algebraically closed field of characteristic $0$. In particular, they classify the finite dimensional irreducible representations and explain how to compute their Gelfand-Tsetlin characters in terms of known characters of standard modules and certain Kazhdan-Lusztig polynomials. The authors' approach exploits the relationship between shifted Yangians and the finite W-algebras associated to nilpotent orbits in general linear Lie algebras.

Noncommutative Maslov Index and Eta-Forms

Author : Charlotte Wahl
Publisher : American Mathematical Soc.
ISBN 13 : 0821839977
Total Pages : 130 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Noncommutative Maslov Index and Eta-Forms by : Charlotte Wahl

Download or read book Noncommutative Maslov Index and Eta-Forms written by Charlotte Wahl and published by American Mathematical Soc.. This book was released on 2007 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author defines and proves a noncommutative generalization of a formula relating the Maslov index of a triple of Lagrangian subspaces of a symplectic vector space to eta-invariants associated to a pair of Lagrangian subspaces. The noncommutative Maslov index, defined for modules over a $C *$-algebra $\mathcal{A}$, is an element in $K_0(\mathcal{A})$. The generalized formula calculates its Chern character in the de Rham homology of certain dense subalgebras of $\mathcal{A}$. The proof is a noncommutative Atiyah-Patodi-Singer index theorem for a particular Dirac operator twisted by an $\mathcal{A}$-vector bundle. The author develops an analytic framework for this type of index problem.

Ramanujan's Forty Identities for the Rogers-Ramanujan Functions

Author : Bruce C. Berndt
Publisher : American Mathematical Soc.
ISBN 13 : 082183973X
Total Pages : 110 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Ramanujan's Forty Identities for the Rogers-Ramanujan Functions by : Bruce C. Berndt

Download or read book Ramanujan's Forty Identities for the Rogers-Ramanujan Functions written by Bruce C. Berndt and published by American Mathematical Soc.. This book was released on 2007 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sir Arthur Conan Doyle's famous fictional detective Sherlock Holmes and his sidekick Dr. Watson go camping and pitch their tent under the stars. During the night, Holmes wakes his companion and says, ``Watson, look up at the stars and tell me what you deduce.'' Watson says, ``I see millions of stars, and it is quite likely that a few of them are planets just like Earth. Therefore there may also be life on these planets.'' Holmes replies, ``Watson, you idiot. Somebody stole ourtent.'' When seeking proofs of Ramanujan's identities for the Rogers-Ramanujan functions, Watson, i.e., G. N. Watson, was not an ``idiot.'' He, L. J. Rogers, and D. M. Bressoud found proofs for several of the identities. A. J. F. Biagioli devised proofs for most (but not all) of the remaining identities.Although some of the proofs of Watson, Rogers, and Bressoud are likely in the spirit of those found by Ramanujan, those of Biagioli are not. in particular, Biagioli used the theory of modular forms. Haunted by the fact that little progress has been made into Ramanujan's insights on these identities in the past 85 years, the present authors sought ``more natural'' proofs. Thus, instead of a missing tent, we have had missing proofs, i.e., Ramanujan's missing proofs of his forty identities for theRogers-Ramanujan functions. in this paper, for 35 of the 40 identities, the authors offer proofs that are in the spirit of Ramanujan. Some of the proofs presented here are due to Watson, Rogers, and Bressoud, but most are new. Moreover, for several identities, the authors present two or threeproofs. For the five identities that they are unable to prove, they provide non-rigorous verifications based on an asymptotic analysis of the associated Rogers-Ramanujan functions. This method, which is related to the 5-dissection of the generating function for cranks found in Ramanujan's lost notebook, is what Ramanujan might have used to discover several of the more difficult identities. Some of the new methods in this paper can be employed to establish new identities for the Rogers-Ramanujanfunctions.

Multivariable Operator Theory

Author : Ernst Albrecht
Publisher : Springer Nature
ISBN 13 : 3031505352
Total Pages : 893 pages
Book Rating : 4.0/5 (315 download)

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Book Synopsis Multivariable Operator Theory by : Ernst Albrecht

Download or read book Multivariable Operator Theory written by Ernst Albrecht and published by Springer Nature. This book was released on 2024-01-22 with total page 893 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the course of his distinguished career, Jörg Eschmeier made a number of fundamental contributions to the development of operator theory and related topics. The chapters in this volume, compiled in his memory, are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.

A Review of Methods for Multivariable Interpolation at Scattered Data Points

Author : M. J. D. Powell
Publisher :
ISBN 13 :
Total Pages : 29 pages
Book Rating : 4.:/5 (475 download)

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Book Synopsis A Review of Methods for Multivariable Interpolation at Scattered Data Points by : M. J. D. Powell

Download or read book A Review of Methods for Multivariable Interpolation at Scattered Data Points written by M. J. D. Powell and published by . This book was released on 1996 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Heisenberg Calculus and Spectral Theory of Hypoelliptic Operators on Heisenberg Manifolds

Author : Raphael Ponge
Publisher : American Mathematical Soc.
ISBN 13 : 0821841483
Total Pages : 150 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Heisenberg Calculus and Spectral Theory of Hypoelliptic Operators on Heisenberg Manifolds by : Raphael Ponge

Download or read book Heisenberg Calculus and Spectral Theory of Hypoelliptic Operators on Heisenberg Manifolds written by Raphael Ponge and published by American Mathematical Soc.. This book was released on 2008 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir deals with the hypoelliptic calculus on Heisenberg manifolds, including CR and contact manifolds. In this context the main differential operators at stake include the Hormander's sum of squares, the Kohn Laplacian, the horizontal sublaplacian, the CR conformal operators of Gover-Graham and the contact Laplacian. These operators cannot be elliptic and the relevant pseudodifferential calculus to study them is provided by the Heisenberg calculus of Beals-Greiner andTaylor.

Maximum Entropy and Bayesian Methods

Author : John Skilling
Publisher : Springer Science & Business Media
ISBN 13 : 9400901070
Total Pages : 327 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Maximum Entropy and Bayesian Methods by : John Skilling

Download or read book Maximum Entropy and Bayesian Methods written by John Skilling and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume records papers given at the fourteenth international maximum entropy conference, held at St John's College Cambridge, England. It seems hard to believe that just thirteen years have passed since the first in the series, held at the University of Wyoming in 1981, and six years have passed since the meeting last took place here in Cambridge. So much has happened. There are two major themes at these meetings, inference and physics. The inference work uses the confluence of Bayesian and maximum entropy ideas to develop and explore a wide range of scientific applications, mostly concerning data analysis in one form or another. The physics work uses maximum entropy ideas to explore the thermodynamic world of macroscopic phenomena. Of the two, physics has the deeper historical roots, and much of the inspiration behind the inference work derives from physics. Yet it is no accident that most of the papers at these meetings are on the inference side. To develop new physics, one must use one's brains alone. To develop inference, computers are used as well, so that the stunning advances in computational power render the field open to rapid advance. Indeed, we have seen a revolution. In the larger world of statistics beyond the maximum entropy movement as such, there is now an explosion of work in Bayesian methods, as the inherent superiority of a defensible and consistent logical structure becomes increasingly apparent in practice.

Operator Algebras, Operator Theory and Applications

Author : J. J. Grobler
Publisher : Springer Science & Business Media
ISBN 13 : 3034601743
Total Pages : 301 pages
Book Rating : 4.0/5 (346 download)

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Book Synopsis Operator Algebras, Operator Theory and Applications by : J. J. Grobler

Download or read book Operator Algebras, Operator Theory and Applications written by J. J. Grobler and published by Springer Science & Business Media. This book was released on 2009-12-24 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the eighteenth International Workshop on Operator Theory and Applications (IWOTA), hosted by the Unit for Business Mathematics and Informatics of North-West University, Potchefstroom, South Africa from July 3 to 6, 2007. The conference (as well as these proceedings) was dedicated to Professors Joseph A. Ball and Marinus M. Kaashoek on the occasion of their 60th and 70th birthdays, respectively. This conference had a particular focus on Von Neumann algebras at the interface of operator theory with functional analysis and on applications of operator theory to differential equations.

Limit Theorems of Polynomial Approximation with Exponential Weights

Author : Michael I. Ganzburg
Publisher : American Mathematical Soc.
ISBN 13 : 0821840630
Total Pages : 178 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Limit Theorems of Polynomial Approximation with Exponential Weights by : Michael I. Ganzburg

Download or read book Limit Theorems of Polynomial Approximation with Exponential Weights written by Michael I. Ganzburg and published by American Mathematical Soc.. This book was released on 2008 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author develops the limit relations between the errors of polynomial approximation in weighted metrics and apply them to various problems in approximation theory such as asymptotically best constants, convergence of polynomials, approximation of individual functions, and multidimensional limit theorems of polynomial approximation.

Operator Theory on Noncommutative Domains

Author : Gelu Popescu
Publisher : American Mathematical Soc.
ISBN 13 : 0821847104
Total Pages : 137 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Operator Theory on Noncommutative Domains by : Gelu Popescu

Download or read book Operator Theory on Noncommutative Domains written by Gelu Popescu and published by American Mathematical Soc.. This book was released on 2010 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Volume 205, number 964 (third of 5 numbers)."

An Operator Perspective on Signals and Systems

Author : Arthur Frazho
Publisher : Springer Science & Business Media
ISBN 13 : 3034602928
Total Pages : 430 pages
Book Rating : 4.0/5 (346 download)

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Book Synopsis An Operator Perspective on Signals and Systems by : Arthur Frazho

Download or read book An Operator Perspective on Signals and Systems written by Arthur Frazho and published by Springer Science & Business Media. This book was released on 2009-12-29 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, we combine operator techniques with state space methods to solve factorization, spectral estimation, and interpolation problems arising in control and signal processing. We present both the theory and algorithms with some Matlab code to solve these problems. A classical approach to spectral factorization problems in control theory is based on Riccati equations arising in linear quadratic control theory and Kalman ?ltering. One advantage of this approach is that it readily leads to algorithms in the non-degenerate case. On the other hand, this approach does not easily generalize to the nonrational case, and it is not always transparent where the Riccati equations are coming from. Operator theory has developed some elegant methods to prove the existence of a solution to some of these factorization and spectral estimation problems in a very general setting. However, these techniques are in general not used to develop computational algorithms. In this monograph, we will use operator theory with state space methods to derive computational methods to solve factorization, sp- tral estimation, and interpolation problems. It is emphasized that our approach is geometric and the algorithms are obtained as a special application of the theory. We will present two methods for spectral factorization. One method derives al- rithms based on ?nite sections of a certain Toeplitz matrix. The other approach uses operator theory to develop the Riccati factorization method. Finally, we use isometric extension techniques to solve some interpolation problems.

Mathematical Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 872 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2007 with total page 872 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Handbook of Image Engineering

Author : Yu-Jin Zhang
Publisher : Springer Nature
ISBN 13 : 9811558736
Total Pages : 1963 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Handbook of Image Engineering by : Yu-Jin Zhang

Download or read book Handbook of Image Engineering written by Yu-Jin Zhang and published by Springer Nature. This book was released on 2021-01-04 with total page 1963 pages. Available in PDF, EPUB and Kindle. Book excerpt: Image techniques have been developed and implemented for various purposes, and image engineering (IE) is a rapidly evolving, integrated discipline comprising the study of all the different branches of image techniques, and encompassing mathematics, physics, biology, physiology, psychology, electrical engineering, computer science and automation. Advances in the field are also closely related to the development of telecommunications, biomedical engineering, remote sensing, surveying and mapping, as well as document processing and industrial applications. IE involves three related and partially overlapping groups of image techniques: image processing (IP) (in its narrow sense), image analysis (IA) and image understanding (IU), and the integration of these three groups makes the discipline of image engineering an important part of the modern information era. This is the first handbook on image engineering, and provides a well-structured, comprehensive overview of this new discipline. It also offers detailed information on the various image techniques. It is a valuable reference resource for R&D professional and undergraduate students involved in image-related activities.