Second Order Sturm Liouville Difference Equations And Orthogonal Polynomials

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Second-Order Sturm-Liouville Difference Equations and Orthogonal Polynomials

Author : Alouf Jirari
Publisher : American Mathematical Soc.
ISBN 13 : 082180359X
Total Pages : 138 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Second-Order Sturm-Liouville Difference Equations and Orthogonal Polynomials by : Alouf Jirari

Download or read book Second-Order Sturm-Liouville Difference Equations and Orthogonal Polynomials written by Alouf Jirari and published by American Mathematical Soc.. This book was released on 1995 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: This well-written book is a timely and significant contribution to the understanding of difference equations. Presenting machinery for analyzing many discrete physical situations, the book will be of interest to physicists and engineers as well as mathematicians. The book develops a theory for regular and singular Sturm-Liouville boundary value problems for difference equations, generalizing many of the known results for differential equations. Discussing the self-adjointness of these problems as well as their abstract spectral resolution in the appropriate $L^2$ setting, the book gives necessary and sufficient conditions for a second-order difference operator to be self-adjoint and have orthogonal polynomials as eigenfunctions. These polynomials are classified into four categories, each of which is given a properties survey and a representative example. Finally, the book shows that the various difference operators defined for these problems are still self-adjoint when restricted to ``energy norms''. This book is suitable as a text for an advanced graduate course on Sturm-Liouville operators or on applied analysis.

Sturm-Liouville Theory

Author : Werner O. Amrein
Publisher : Springer Science & Business Media
ISBN 13 : 9783764370664
Total Pages : 364 pages
Book Rating : 4.3/5 (76 download)

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Book Synopsis Sturm-Liouville Theory by : Werner O. Amrein

Download or read book Sturm-Liouville Theory written by Werner O. Amrein and published by Springer Science & Business Media. This book was released on 2005-05-19 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of survey articles based on lectures presented at a colloquium and workshop in Geneva in 2003 to commemorate the 200th anniversary of the birth of Charles François Sturm. It aims at giving an overview of the development of Sturm-Liouville theory from its historical roots to present day research. It is the first time that such a comprehensive survey has been made available in compact form. The contributions come from internationally renowned experts and cover a wide range of developments of the theory. The book can therefore serve both as an introduction to Sturm-Liouville theory and as background for ongoing research. The volume is addressed to researchers in related areas, to advanced students and to those interested in the historical development of mathematics. The book will also be of interest to those involved in applications of the theory to diverse areas such as engineering, fluid dynamics and computational spectral analysis.

Special Functions and Generalized Sturm-Liouville Problems

Author : Mohammad Masjed-Jamei
Publisher : Springer Nature
ISBN 13 : 3030328201
Total Pages : 322 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Special Functions and Generalized Sturm-Liouville Problems by : Mohammad Masjed-Jamei

Download or read book Special Functions and Generalized Sturm-Liouville Problems written by Mohammad Masjed-Jamei and published by Springer Nature. This book was released on 2020-01-25 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses theoretical and applied aspects of Sturm-Liouville theory and its generalization. It introduces and classifies generalized Sturm-Liouville problems in three different spaces: continuous, discrete, and q-discrete spaces, focusing on special functions that are solutions of a regular or singular Sturm-Liouville problem. Further, it describes the conditions under which the usual Sturm-Liouville problems with symmetric solutions can be extended to a larger class, particularly highlighting the solutions of generalized problems that result in new orthogonal sequences of continuous or discrete functions. Sturm-Liouville theory is central to problems in many areas, such as engineering, mathematics, physics, and biology. This accessibly written book on the topic is a valuable resource for a broad interdisciplinary readership, from novices to experts.

Orthogonal Polynomials

Author : Mama Foupouagnigni
Publisher : Springer Nature
ISBN 13 : 3030367444
Total Pages : 683 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Orthogonal Polynomials by : Mama Foupouagnigni

Download or read book Orthogonal Polynomials written by Mama Foupouagnigni and published by Springer Nature. This book was released on 2020-03-11 with total page 683 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents contributions of international and local experts from the African Institute for Mathematical Sciences (AIMS-Cameroon) and also from other local universities in the domain of orthogonal polynomials and applications. The topics addressed range from univariate to multivariate orthogonal polynomials, from multiple orthogonal polynomials and random matrices to orthogonal polynomials and Painlevé equations. The contributions are based on lectures given at the AIMS-Volkswagen Stiftung Workshop on Introduction of Orthogonal Polynomials and Applications held on October 5–12, 2018 in Douala, Cameroon. This workshop, funded within the framework of the Volkswagen Foundation Initiative "Symposia and Summer Schools", was aimed globally at promoting capacity building in terms of research and training in orthogonal polynomials and applications, discussions and development of new ideas as well as development and enhancement of networking including south-south cooperation.

Frontiers In Orthogonal Polynomials And Q-series

Author : Nashed M Zuhair
Publisher : World Scientific
ISBN 13 : 981322889X
Total Pages : 576 pages
Book Rating : 4.8/5 (132 download)

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

Download or read book Frontiers In Orthogonal Polynomials And Q-series written by Nashed M Zuhair and published by World Scientific. This book was released on 2018-01-12 with total page 576 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. Contents: Mourad Ismail (Richard Askey)Binomial Andrews–Gordon–Bressoud Identities (Dennis Stanton)Symmetric Expansions of Very Well-Poised Basic Hypergeometric Series (George E Andrews)A Sturm–Liouville Theory for Hahn Difference Operator (M H Annaby, A E Hamza and S D Makharesh)Solvability of the Hankel Determinant Problem for Real Sequences (Andrew Bakan and Christian Berg)Convolution and Product Theorems for the Special Affine Fourier Transform (Ayush Bhandari and Ahmed I Zayed)A Further Look at Time-and-Band Limiting for Matrix Orthogonal Polynomials (M Castro, F A Grünbaum, I Pacharoni and I Zurrián)The Orthogonality of Al–Salam–Carlitz Polynomials for Complex Parameters (Howard S Cohl, Roberto S Costas-Santos and Wenqing Xu)Crouching AGM, Hidden Modularity (Shaun Cooper, Jesús Guillera, Armin Straub and Wadim Zudilin)Asymptotics of Orthogonal Polynomials and the Painlevé Transcendents (Dan Dai)From the Gaussian Circle Problem to Multivariate Shannon Sampling (Willi Freeden and M Zuhair Nashed)Weighted Partition Identities and Divisor Sums (F G Garvan)On the Ismail–Letessier–Askey Monotonicity Conjecture for Zeros of Ultraspherical Polynomials (Walter Gautschi)A Discrete Top-Down Markov Problem in Approximation Theory (Walter Gautschi)Supersymmetry of the Quantum Rotor (Vincent X Genest, Luc Vinet, Guo-Fu Yu and Alexei Zhedanov)The Method of Brackets in Experimental Mathematics (Ivan Gonzalez, Karen Kohl, Lin Jiu and Victor H Moll)Balanced Modular Parameterizations (Tim Huber, Danny Lara and Esteban Melendez)Some Smallest Parts Functions from Variations of Bailey's Lemma (Chris Jennings-Shaffer)Dual Addition Formulas Associated with Dual Product Formulas (Tom H Koornwinder)Holonomic Tools for Basic Hypergeometric Functions (Christoph Koutschan and Peter Paule)A Direct Evaluation of an Integral of Ismail and Valent (Alexey Kuznetsov)Algebraic Generating Functions for Gegenbauer Polynomials (Robert S Maier)q-Analogues of Two Product Formulas of Hypergeometric Functions by Bailey (Michael J Schlosser)Summation Formulae for Noncommutative Hypergeometric Series (Michael J Schlosser)Asymptotics of Generalized Hypergeometric Functions (Y Lin and R Wong)Mock Theta-Functions of the Third Order of Ramanujan in Terms of Appell–Lerch Series (Changgui Zhang)On Certain Positive Semidefinite Matrices of Special Functions (Ruiming Zhang) Readership: Graduate students and researchers interested in orthogonal polynomials and

Difference Equations, Special Functions and Orthogonal Polynomials

Author : Saber Elaydi
Publisher : World Scientific
ISBN 13 : 9812706437
Total Pages : 789 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Difference Equations, Special Functions and Orthogonal Polynomials by : Saber Elaydi

Download or read book Difference Equations, Special Functions and Orthogonal Polynomials written by Saber Elaydi and published by World Scientific. This book was released on 2007 with total page 789 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains talks given at a joint meeting of three communities working in the fields of difference equations, special functions and applications (ISDE, OPSFA, and SIDE). The articles reflect the diversity of the topics in the meeting but have difference equations as common thread. Articles cover topics in difference equations, discrete dynamical systems, special functions, orthogonal polynomials, symmetries, and integrable difference equations.

Difference Equations, Special Functions and Orthogonal Polynomials

Author :
Publisher :
ISBN 13 : 9814475467
Total Pages : pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Difference Equations, Special Functions and Orthogonal Polynomials by :

Download or read book Difference Equations, Special Functions and Orthogonal Polynomials written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Analysis and Applications

Author : Ravi P. Agarwal
Publisher : Springer Science & Business Media
ISBN 13 : 9781402017124
Total Pages : 378 pages
Book Rating : 4.0/5 (171 download)

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Book Synopsis Nonlinear Analysis and Applications by : Ravi P. Agarwal

Download or read book Nonlinear Analysis and Applications written by Ravi P. Agarwal and published by Springer Science & Business Media. This book was released on 2003 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is dedicated to Professor V. Lakshmikantham on the occasion of his 80th birthday. The volumes consist of 45 research papers from distinguished experts from a variety of research areas. Topics include monotonicity and compact methods, blow up and global existence for hyperbolic problems, dynamic systems on time scales, maximum monotone mappings, fixed point theory, quasivalued elliptic problems including mixed BVP's, impulsive and evolution inclusions, iterative processes, Morse theory, hemivariational inequalities, Navier-Stokes equations, multivalued BVP's, various aspects of control theory, integral operators, semigroup theories, modelling of real world phenomena, higher order parabolic equations, invariant measures, superlinear problems and operator equations.

Symmetries and Integrability of Difference Equations

Author : Decio Levi
Publisher : Cambridge University Press
ISBN 13 : 1139493841
Total Pages : 361 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Symmetries and Integrability of Difference Equations by : Decio Levi

Download or read book Symmetries and Integrability of Difference Equations written by Decio Levi and published by Cambridge University Press. This book was released on 2011-06-23 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to the subject suitable for graduate students and researchers. This book is also an up-to-date survey of the current state of the art and thus will serve as a valuable reference for specialists in the field.

Orthogonal Polynomials

Author : Paul Nevai
Publisher : Springer Science & Business Media
ISBN 13 : 9400905017
Total Pages : 472 pages
Book Rating : 4.4/5 (9 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 Science & Business Media. This book was released on 2012-12-06 with total page 472 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.

Difference Equations, Special Functions and Orthogonal Polynomials

Author : Saber Elaydi
Publisher : World Scientific
ISBN 13 : 9812770755
Total Pages : 789 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Difference Equations, Special Functions and Orthogonal Polynomials by : Saber Elaydi

Degenerate Principal Series for Symplectic and Odd-Orthogonal Groups

Author : Chris Jantzen
Publisher : American Mathematical Soc.
ISBN 13 : 0821804820
Total Pages : 114 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Degenerate Principal Series for Symplectic and Odd-Orthogonal Groups by : Chris Jantzen

Download or read book Degenerate Principal Series for Symplectic and Odd-Orthogonal Groups written by Chris Jantzen and published by American Mathematical Soc.. This book was released on 1996-01-01 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir studies reducibility in a certain class of induced representations for and , where is -adic. In particular, it is concerned with representations obtained by inducing a one-dimensional representation from a maximal parabolic subgroup (i.e., degenerate principal series representations). Using the Jacquet module techniques of Tadić, the reducibility points for such representations are determined. When reducible, the composition series is described, giving Langlands data and Jacquet modules for the irreducible composition factors.

The Method of Layer Potentials for the Heat Equation in Time-Varying Domains

Author : John L. Lewis
Publisher : American Mathematical Soc.
ISBN 13 : 0821803603
Total Pages : 157 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Method of Layer Potentials for the Heat Equation in Time-Varying Domains by : John L. Lewis

Download or read book The Method of Layer Potentials for the Heat Equation in Time-Varying Domains written by John L. Lewis and published by American Mathematical Soc.. This book was released on 1995 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent years have seen renewed interest in the solution of parabolic boundary value problems by the method of layer potentials, a method that has been extraordinarily useful in the solution of elliptic problems. This book develops this method for the heat equation in time-varying domains. In the first chapter, Lewis and Murray show that certain singular integral operators on $L^p$ are bounded. In the second chapter, they develop a modification of the David buildup scheme, as well as some extension theorems, to obtain $L^p$ boundedness of the double layer heat potential on the boundary of the domains. The third chapter uses the results of the first two, along with a buildup scheme, to show the mutual absolute continuity of parabolic measure and a certain projective Lebesgue measure. Lewis and Murray also obtain $A_\infty$ results and discuss the Dirichlet and Neumann problems for a certain subclass of the domains.

Degree 16 Standard L-function of GSp(2) XGSp(2)

Author : Dihua Jiang
Publisher : American Mathematical Soc.
ISBN 13 : 0821804766
Total Pages : 196 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Degree 16 Standard L-function of GSp(2) XGSp(2) by : Dihua Jiang

Download or read book Degree 16 Standard L-function of GSp(2) XGSp(2) written by Dihua Jiang and published by American Mathematical Soc.. This book was released on 1996 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Automorphic L-functions, introduced by Robert Langlands in the 1960s, are natural extensions of such classical L-functions as the Riemann zeta function, Hecke L-functions, etc. They form an important part of the Langlands Program, which seeks to establish connections among number theory, representation theory, and geometry. This book offers, via the Rankin-Selberg method, a thorough and comprehensive examination of the degree 16 standard L-function of the product of two rank two symplectic similitude groups, which includes the study of the global integral of Rankin-Selberg type and local integrals, analytic properties of certain Eisenstein series of symplectic groups, and the relevant residue representations.

Inverse Sturm-Liouville Problems

Author : B. M. Levitan
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110941937
Total Pages : 252 pages
Book Rating : 4.1/5 (19 download)

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Book Synopsis Inverse Sturm-Liouville Problems by : B. M. Levitan

Download or read book Inverse Sturm-Liouville Problems written by B. M. Levitan and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-07-12 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interest in inverse problems of spectral analysis has increased considerably in recent years due to the applications to important non-linear equations in mathematical physics. This monograph is devoted to the detailed theory of inverse problems and methods of their solution for the Sturm-Liouville case. Chapters 1--6 contain proofs which are, in many cases, very different from those known earlier. Chapters 4--6 are devoted to inverse problems of quantum scattering theory with attention being focused on physical applications. Chapters 7--11 are based on the author's recent research on the theory of finite- and infinite-zone potentials. A chapter discussing the applications to the Korteweg--de Vries problem is also included. This monograph is important reading for all researchers in the field of mathematics and physics.

Textile Systems for Endomorphisms and Automorphisms of the Shift

Author : Masakazu Nasu
Publisher : American Mathematical Soc.
ISBN 13 : 0821826069
Total Pages : 215 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Textile Systems for Endomorphisms and Automorphisms of the Shift by : Masakazu Nasu

Download or read book Textile Systems for Endomorphisms and Automorphisms of the Shift written by Masakazu Nasu and published by American Mathematical Soc.. This book was released on 1995 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the major topics in symbolic dynamics is the analysis of the dynamical systems defined by endomorphisms and automorphisms of subshifts. This includes analysis of the dynamical behavior of one-dimensional cellular automata as a special case. In this work, Nasu introduces the notion of a textile system, which is useful in analyzing the dynamical systems defined by endomorphisms and automorphisms of topological Markov shifts, including one-sided ones. The dynamical properties of automorphisms of sofic systems are also studied. Requiring few prerequisites, this work will appeal not only to specialists in symbolic dynamics but also to nonspecialists interested in symbolic dynamics and those interested in analysis of the dynamical behavior of cellular automata.

Tilting in Abelian Categories and Quasitilted Algebras

Author : Dieter Happel
Publisher : American Mathematical Soc.
ISBN 13 : 0821804448
Total Pages : 88 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Tilting in Abelian Categories and Quasitilted Algebras by : Dieter Happel

Download or read book Tilting in Abelian Categories and Quasitilted Algebras written by Dieter Happel and published by American Mathematical Soc.. This book was released on 1996 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the authors generalize with respect to a tilting module of projective dimension at most one for an artin algebra to tilting with respect to a torsion pair in an abelian category. A general theory is developed for such tilting and the reader is led to a generalization for tilted algebras which the authors call ``quasitilted algebras''. This class also contains the canonical algebras, and the authors show that the quasitilted algebras are characterized by having global dimension at most two and each indecomposable module having projective dimension at most one or injective dimension at most one. The authors also give other characterizations of quasitilted algebras and give methods for constructing such algebras. In particular, they investigate when one-point extensions of hereditary algebras are quasitilted.