From Operator Theory To Orthogonal Polynomials Combinatorics And Number Theory

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From Operator Theory to Orthogonal Polynomials, Combinatorics, and Number Theory

Author : Fritz Gesztesy
Publisher : Springer Nature
ISBN 13 : 3030754251
Total Pages : 388 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis From Operator Theory to Orthogonal Polynomials, Combinatorics, and Number Theory by : Fritz Gesztesy

Download or read book From Operator Theory to Orthogonal Polynomials, Combinatorics, and Number Theory written by Fritz Gesztesy and published by Springer Nature. This book was released on 2021-11-11 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main topics of this volume, dedicated to Lance Littlejohn, are operator and spectral theory, orthogonal polynomials, combinatorics, number theory, and the various interplays of these subjects. Although the event, originally scheduled as the Baylor Analysis Fest, had to be postponed due to the pandemic, scholars from around the globe have contributed research in a broad range of mathematical fields. The collection will be of interest to both graduate students and professional mathematicians. Contributors are: G.E. Andrews, B.M. Brown, D. Damanik, M.L. Dawsey, W.D. Evans, J. Fillman, D. Frymark, A.G. García, L.G. Garza, F. Gesztesy, D. Gómez-Ullate, Y. Grandati, F.A. Grünbaum, S. Guo, M. Hunziker, A. Iserles, T.F. Jones, K. Kirsten, Y. Lee, C. Liaw, F. Marcellán, C. Markett, A. Martinez-Finkelshtein, D. McCarthy, R. Milson, D. Mitrea, I. Mitrea, M. Mitrea, G. Novello, D. Ong, K. Ono, J.L. Padgett, M.M.M. Pang, T. Poe, A. Sri Ranga, K. Schiefermayr, Q. Sheng, B. Simanek, J. Stanfill, L. Velázquez, M. Webb, J. Wilkening, I.G. Wood, M. Zinchenko.

Orthogonal Polynomials on the Unit Circle: Spectral theory

Author : Barry Simon
Publisher : American Mathematical Soc.
ISBN 13 : 9780821836750
Total Pages : 608 pages
Book Rating : 4.8/5 (367 download)

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Book Synopsis Orthogonal Polynomials on the Unit Circle: Spectral theory by : Barry Simon

Download or read book Orthogonal Polynomials on the Unit Circle: Spectral theory written by Barry Simon and published by American Mathematical Soc.. This book was released on 2005 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. This book discusses topics such as asymptotics of Toeplitz determinants (Szego's theorems), and limit theorems for the density of the zeros of orthogonal polynomials.

Symmetric Functions and Combinatorial Operators on Polynomials

Author : Alain Lascoux
Publisher : American Mathematical Soc.
ISBN 13 : 0821828711
Total Pages : 282 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Symmetric Functions and Combinatorial Operators on Polynomials by : Alain Lascoux

Download or read book Symmetric Functions and Combinatorial Operators on Polynomials written by Alain Lascoux and published by American Mathematical Soc.. This book was released on 2003 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of symmetric functions is an old topic in mathematics, which is used as an algebraic tool in many classical fields. With $\lambda$-rings, one can regard symmetric functions as operators on polynomials and reduce the theory to just a handful of fundamental formulas. One of the main goals of the book is to describe the technique of $\lambda$-rings. The main applications of this technique to the theory of symmetric functions are related to the Euclid algorithm and its occurrence in division, continued fractions, Pade approximants, and orthogonal polynomials. Putting the emphasis on the symmetric group instead of symmetric functions, one can extend the theory to non-symmetric polynomials, with Schur functions being replaced by Schubert polynomials. In two independent chapters, the author describes the main properties of these polynomials, following either the approach of Newton and interpolation methods, or the method of Cauchy and the diagonalization of a kernel generalizing the resultant. The last chapter sketches a non-commutative version of symmetric functions, with the help of Young tableaux and the plactic monoid. The book also contains numerous exercises clarifying and extending many points of the main text.

Orthogonal Matrix-valued Polynomials and Applications

Author : Israel Gohberg
Publisher : Birkhauser
ISBN 13 :
Total Pages : 232 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Orthogonal Matrix-valued Polynomials and Applications by : Israel Gohberg

Download or read book Orthogonal Matrix-valued Polynomials and Applications written by Israel Gohberg and published by Birkhauser. This book was released on 1988 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Orthogonal Systems and Convolution Operators

Author : Robert Ellis
Publisher : Springer Science & Business Media
ISBN 13 : 9783764369293
Total Pages : 264 pages
Book Rating : 4.3/5 (692 download)

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Book Synopsis Orthogonal Systems and Convolution Operators by : Robert Ellis

Download or read book Orthogonal Systems and Convolution Operators written by Robert Ellis and published by Springer Science & Business Media. This book was released on 2003 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main concern of this book is the distribution of zeros of polynomials that are orthogonal on the unit circle with respect to an indefinite weighted scalar or inner product. The first theorem of this type, proved by M. G. Krein, was a far-reaching generalization of G. Szegö's result for the positive definite case. A continuous analogue of that theorem was proved by Krein and H. Langer. These results, as well as many generalizations and extensions, are thoroughly treated in this book. A unifying theme is the general problem of orthogonalization with invertible squares in modules over C*-algebras. Particular modules that are considered in detail include modules of matrices, matrix polynomials, matrix-valued functions, linear operators, and others. One of the central features of this book is the interplay between orthogonal polynomials and their generalizations on the one hand, and operator theory, especially the theory of Toeplitz marices and operators, and Fredholm and Wiener-Hopf operators, on the other hand. The book is of interest to both engineers and specialists in analysis.

Frontiers In Orthogonal Polynomials And Q-series

Author : M Zuhair Nashed
Publisher : World Scientific
ISBN 13 : 981322889X
Total Pages : 577 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Frontiers In Orthogonal Polynomials And Q-series by : M Zuhair Nashed

Download or read book Frontiers In Orthogonal Polynomials And Q-series written by M Zuhair Nashed and published by World Scientific. This book was released on 2018-01-12 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume aims to highlight trends and important directions of research in orthogonal polynomials, q-series, and related topics in number theory, combinatorics, approximation theory, mathematical physics, and computational and applied harmonic analysis. This collection is based on the invited lectures by well-known contributors from the International Conference on Orthogonal Polynomials and q-Series, that was held at the University of Central Florida in Orlando, on May 10-12, 2015. The conference was dedicated to Professor Mourad Ismail on his 70th birthday.The editors strived for a volume that would inspire young researchers and provide a wealth of information in an engaging format. Theoretical, combinatorial and computational/algorithmic aspects are considered, and each chapter contains many references on its topic, when appropriate.

Orthogonal Polynomials

Author : Paul Nevai
Publisher : Springer
ISBN 13 : 9789401067119
Total Pages : 488 pages
Book Rating : 4.0/5 (671 download)

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Book Synopsis Orthogonal Polynomials by : Paul Nevai

Download or read book Orthogonal Polynomials written by Paul Nevai and published by Springer. This book was released on 2011-09-20 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the Proceedings of the NATO Advanced Study Institute on "Orthogonal Polynomials and Their Applications" held at The Ohio State University in Columbus, Ohio, U.S.A. between May 22,1989 and June 3,1989. The Advanced Study Institute primarily concentrated on those aspects of the theory and practice of orthogonal polynomials which surfaced in the past decade when the theory of orthogonal polynomials started to experience an unparalleled growth. This progress started with Richard Askey's Regional Confer ence Lectures on "Orthogonal Polynomials and Special Functions" in 1975, and subsequent discoveries led to a substantial revaluation of one's perceptions as to the nature of orthogonal polynomials and their applicability. The recent popularity of orthogonal polynomials is only partially due to Louis de Branges's solution of the Bieberbach conjecture which uses an inequality of Askey and Gasper on Jacobi polynomials. The main reason lies in their wide applicability in areas such as Pade approximations, continued fractions, Tauberian theorems, numerical analysis, probability theory, mathematical statistics, scattering theory, nuclear physics, solid state physics, digital signal processing, electrical engineering, theoretical chemistry and so forth. This was emphasized and convincingly demonstrated during the presentations by both the principal speakers and the invited special lecturers. The main subjects of our Advanced Study Institute included complex orthogonal polynomials, signal processing, the recursion method, combinatorial interpretations of orthogonal polynomials, computational problems, potential theory, Pade approximations, Julia sets, special functions, quantum groups, weighted approximations, orthogonal polynomials associated with root systems, matrix orthogonal polynomials, operator theory and group representations.

Orthogonal Polynomials on the Unit Circle

Author : Barry Simon
Publisher : American Mathematical Soc.
ISBN 13 : 082184864X
Total Pages : 610 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Orthogonal Polynomials on the Unit Circle by : Barry Simon

Download or read book Orthogonal Polynomials on the Unit Circle written by Barry Simon and published by American Mathematical Soc.. This book was released on 2005 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-part volume gives a comprehensive overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. A major theme involves the connections between the Verblunsky coefficients (the coefficients of the recurrence equation for the orthogonal polynomials) and the measures, an analog of the spectral theory of one-dimensional Schrödinger operators. Among the topics discussed along the way are the asymptotics of Toeplitz determinants (Szegő's theorems), limit theorems for the density of the zeros of orthogonal polynomials, matrix representations for multiplication by (CMV matrices), periodic Verblunsky coefficients from the point of view of meromorphic functions on hyperelliptic surfaces, and connections between the theories of orthogonal polynomials on the unit circle and on the real line. The book is suitable for graduate students and researchers interested in analysis.

From Complex Analysis to Operator Theory: A Panorama

Author : Malcolm Brown
Publisher : Springer Nature
ISBN 13 : 3031311396
Total Pages : 731 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis From Complex Analysis to Operator Theory: A Panorama by : Malcolm Brown

Download or read book From Complex Analysis to Operator Theory: A Panorama written by Malcolm Brown and published by Springer Nature. This book was released on 2023-09-21 with total page 731 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the memory of Sergey Naboko (1950-2020). In addition to original research contributions covering the vast areas of interest of Sergey Naboko, it includes personal reminiscences and comments on the works and legacy of Sergey Naboko’s scientific achievements. Areas from complex analysis to operator theory, especially, spectral theory, are covered, and the papers will inspire current and future researchers in these areas.

Orthogonal Polynomials

Author : Paul Nevai
Publisher :
ISBN 13 : 9789400905023
Total Pages : 488 pages
Book Rating : 4.9/5 (5 download)

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Book Synopsis Orthogonal Polynomials by : Paul Nevai

Download or read book Orthogonal Polynomials written by Paul Nevai and published by . This book was released on 1989-12-31 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Arithmetical Investigations

Author : Shai M. J. Haran
Publisher : Springer
ISBN 13 : 3540783792
Total Pages : 224 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Arithmetical Investigations by : Shai M. J. Haran

Download or read book Arithmetical Investigations written by Shai M. J. Haran and published by Springer. This book was released on 2008-04-25 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume the author further develops his philosophy of quantum interpolation between the real numbers and the p-adic numbers. The p-adic numbers contain the p-adic integers Zp which are the inverse limit of the finite rings Z/pn. This gives rise to a tree, and probability measures w on Zp correspond to Markov chains on this tree. From the tree structure one obtains special basis for the Hilbert space L2(Zp,w). The real analogue of the p-adic integers is the interval [-1,1], and a probability measure w on it gives rise to a special basis for L2([-1,1],w) - the orthogonal polynomials, and to a Markov chain on "finite approximations" of [-1,1]. For special (gamma and beta) measures there is a "quantum" or "q-analogue" Markov chain, and a special basis, that within certain limits yield the real and the p-adic theories. This idea can be generalized variously. In representation theory, it is the quantum general linear group GLn(q)that interpolates between the p-adic group GLn(Zp), and between its real (and complex) analogue -the orthogonal On (and unitary Un )groups. There is a similar quantum interpolation between the real and p-adic Fourier transform and between the real and p-adic (local unramified part of) Tate thesis, and Weil explicit sums.

Algebraic Combinatorics

Author : Chris Godsil
Publisher : Routledge
ISBN 13 : 1351467514
Total Pages : 368 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Algebraic Combinatorics by : Chris Godsil

Download or read book Algebraic Combinatorics written by Chris Godsil and published by Routledge. This book was released on 2017-10-19 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate level text is distinguished both by the range of topics and the novelty of the material it treats--more than half of the material in it has previously only appeared in research papers. The first half of this book introduces the characteristic and matchings polynomials of a graph. It is instructive to consider these polynomials together because they have a number of properties in common. The matchings polynomial has links with a number of problems in combinatorial enumeration, particularly some of the current work on the combinatorics of orthogonal polynomials. This connection is discussed at some length, and is also in part the stimulus for the inclusion of chapters on orthogonal polynomials and formal power series. Many of the properties of orthogonal polynomials are derived from properties of characteristic polynomials. The second half of the book introduces the theory of polynomial spaces, which provide easy access to a number of important results in design theory, coding theory and the theory of association schemes. This book should be of interest to second year graduate text/reference in mathematics.

Orthogonal Polynomials and Special Functions

Author : Erik Koelink
Publisher : Springer
ISBN 13 : 3540449450
Total Pages : 259 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Orthogonal Polynomials and Special Functions by : Erik Koelink

Download or read book Orthogonal Polynomials and Special Functions written by Erik Koelink and published by Springer. This book was released on 2003-07-03 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: The set of lectures from the Summer School held in Leuven in 2002 provide an up-to-date account of recent developments in orthogonal polynomials and special functions, in particular for algorithms for computer algebra packages, 3nj-symbols in representation theory of Lie groups, enumeration, multivariable special functions and Dunkl operators, asymptotics via the Riemann-Hilbert method, exponential asymptotics and the Stokes phenomenon. Thenbsp;volume aims at graduate students and post-docs working in the field of orthogonal polynomials and special functions, and in related fields interacting with orthogonal polynomials, such as combinatorics, computer algebra, asymptotics, representation theory, harmonic analysis, differential equations, physics. The lectures are self-contained requiring onlynbsp;a basic knowledge of analysis and algebra, and each includes many exercises.

Lectures on Orthogonal Polynomials and Special Functions

Author : Howard S. Cohl
Publisher : Cambridge University Press
ISBN 13 : 1108821596
Total Pages : 351 pages
Book Rating : 4.1/5 (88 download)

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Book Synopsis Lectures on Orthogonal Polynomials and Special Functions by : Howard S. Cohl

Download or read book Lectures on Orthogonal Polynomials and Special Functions written by Howard S. Cohl and published by Cambridge University Press. This book was released on 2020-10-15 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains graduate-level introductions by international experts to five areas of research in orthogonal polynomials and special functions.

Symmetric Functions and Orthogonal Polynomials

Author : Ian Grant Macdonald
Publisher : American Mathematical Soc.
ISBN 13 : 0821807706
Total Pages : 71 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Symmetric Functions and Orthogonal Polynomials by : Ian Grant Macdonald

Download or read book Symmetric Functions and Orthogonal Polynomials written by Ian Grant Macdonald and published by American Mathematical Soc.. This book was released on 1998 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most classical areas of algebra, the theory of symmetric functions and orthogonal polynomials, has long been known to be connected to combinatorics, representation theory and other branches of mathematics. Written by perhaps the most famous author on the topic, this volume explains some of the current developments regarding these connections. It is based on lectures presented by the author at Rutgers University. Specifically, he gives recent results on orthogonal polynomials associated with affine Hecke algebras, surveying the proofs of certain famous combinatorial conjectures.

An Introduction to Operator Polynomials

Author : I. Gohberg
Publisher : Birkhäuser
ISBN 13 : 3034891520
Total Pages : 401 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis An Introduction to Operator Polynomials by : I. Gohberg

Download or read book An Introduction to Operator Polynomials written by I. Gohberg and published by Birkhäuser. This book was released on 2012-12-06 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the modern theory of polynomials whose coefficients are linear bounded operators in a Banach space - operator polynomials. This theory has its roots and applications in partial differential equations, mechanics and linear systems, as well as in modern operator theory and linear algebra. Over the last decade, new advances have been made in the theory of operator polynomials based on the spectral approach. The author, along with other mathematicians, participated in this development, and many of the recent results are reflected in this monograph. It is a pleasure to acknowledge help given to me by many mathematicians. First I would like to thank my teacher and colleague, I. Gohberg, whose guidance has been invaluable. Throughout many years, I have worked wtih several mathematicians on the subject of operator polynomials, and, consequently, their ideas have influenced my view of the subject; these are I. Gohberg, M. A. Kaashoek, L. Lerer, C. V. M. van der Mee, P. Lancaster, K. Clancey, M. Tismenetsky, D. A. Herrero, and A. C. M. Ran. The following mathematicians gave me advice concerning various aspects of the book: I. Gohberg, M. A. Kaashoek, A. C. M. Ran, K. Clancey, J. Rovnyak, H. Langer, P.

Computer Algebra and Polynomials

Author : Jaime Gutierrez
Publisher : Springer
ISBN 13 : 3319150812
Total Pages : 222 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Computer Algebra and Polynomials by : Jaime Gutierrez

Download or read book Computer Algebra and Polynomials written by Jaime Gutierrez and published by Springer. This book was released on 2015-01-20 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebra and number theory have always been counted among the most beautiful mathematical areas with deep proofs and elegant results. However, for a long time they were not considered that important in view of the lack of real-life applications. This has dramatically changed: nowadays we find applications of algebra and number theory frequently in our daily life. This book focuses on the theory and algorithms for polynomials over various coefficient domains such as a finite field or ring. The operations on polynomials in the focus are factorization, composition and decomposition, basis computation for modules, etc. Algorithms for such operations on polynomials have always been a central interest in computer algebra, as it combines formal (the variables) and algebraic or numeric (the coefficients) aspects. The papers presented were selected from the Workshop on Computer Algebra and Polynomials, which was held in Linz at the Johann Radon Institute for Computational and Applied Mathematics (RICAM) during November 25-29, 2013, at the occasion of the Special Semester on Applications of Algebra and Number Theory.