Download or read book Coimbra Lecture Notes on Orthogonal Polynomials written by Amilcar Jose Pinto Lopes Branquinho and published by Nova Publishers. This book was released on 2008 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Orthogonal Polynomials and Special Functions (OPSF) have a very rich history, going back to 19th century when mathematicians and physicists tried to solve the most important deferential equations of mathematical physics. Hermite-Padé approximation was also introduced at that time, to prove the transcendence of the remarkable constant e (the basis of the natural logarithm). Since then OPSF has developed to a standard subject within mathematics, which is driven by applications. The applications are numerous, both within mathematics (e.g. statistics, combinatory, harmonic analysis, number theory) and other sciences, such as physics, biology, computer science, chemistry. The main reason for the fact that OPSF has been so successful over the centuries is its usefulness in other branches of mathematics and physics, as well as other sciences. There are many different aspects of OPSF. Some of the most important developments for OPSF are related to the theory of rational approximation of analytic functions, in particular the extension to simultaneous rational approximation to a system of functions. Important tools for rational approximation are Riemann-Hilbert problems, the theory of orthogonal polynomials, logarithmic potential theory, and operator theory for difference operators. This new book presents the latest research in the field.
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 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by experts in their respective fields, this collection of pedagogic surveys provides detailed insight and background into five separate areas at the forefront of modern research in orthogonal polynomials and special functions at a level suited to graduate students. A broad range of topics are introduced including exceptional orthogonal polynomials, q-series, applications of spectral theory to special functions, elliptic hypergeometric functions, and combinatorics of orthogonal polynomials. Exercises, examples and some open problems are provided. The volume is derived from lectures presented at the OPSF-S6 Summer School at the University of Maryland, and has been carefully edited to provide a coherent and consistent entry point for graduate students and newcomers.
Download or read book A First Course on Orthogonal Polynomials written by Kenier Castillo and published by CRC Press. This book was released on 2024-11-19 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: A First Course on Orthogonal Polynomials: Classical Orthogonal Polynomials and Related Topics provides an introduction to orthogonal polynomials and special functions aimed at graduate students studying these topics for the first time. A large part of its content is essentially inspired by the works of Pascal Maroni on the so-called algebraic theory of orthogonal polynomials, which distinguishes it from other contributions in the field. Features Suitable for a graduate course in orthogonal polynomials Can be used for a short course on the algebraic theory of orthogonal polynomials and its applicability to the study of the “old” classical orthogonal polynomials Includes numerous exercises for each topic Real and complex analysis are the only prerequisites
Download or read book Complex Function Theory Operator Theory Schur Analysis and Systems Theory written by Daniel Alpay and published by Springer Nature. This book was released on 2020-09-19 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is dedicated to Victor Emmanuilovich Katsnelson on the occasion of his 75th birthday and celebrates his broad mathematical interests and contributions.Victor Emmanuilovich’s mathematical career has been based mainly at the Kharkov University and the Weizmann Institute. However, it also included a one-year guest professorship at Leipzig University in 1991, which led to him establishing close research contacts with the Schur analysis group in Leipzig, a collaboration that still continues today. Reflecting these three periods in Victor Emmanuilovich's career, present and former colleagues have contributed to this book with research inspired by him and presentations on their joint work. Contributions include papers in function theory (Favorov-Golinskii, Friedland-Goldman-Yomdin, Kheifets-Yuditskii) , Schur analysis, moment problems and related topics (Boiko-Dubovoy, Dyukarev, Fritzsche-Kirstein-Mädler), extension of linear operators and linear relations (Dijksma-Langer, Hassi-de Snoo, Hassi -Wietsma) and non-commutative analysis (Ball-Bolotnikov, Cho-Jorgensen).
Download or read book Laredo Lectures on Orthogonal Polynomials and Special Functions written by Renato Alvarez-Nodarse and published by Nova Publishers. This book was released on 2004 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new book presents research in orthogonal polynomials and special functions. Recent developments in the theory and accomplishments of the last decade are pointed out and directions for research in the future are identified. The topics covered include matrix orthogonal polynomials, spectral theory and special functions, Asymptotics for orthogonal polynomials via Riemann-Hilbert methods, Polynomial wavelets and Koornwinder polynomials.
Download or read book Orthogonal Polynomials Current Trends and Applications written by Francisco Marcellán and published by Springer Nature. This book was released on 2021 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume contains the Proceedings of the Seventh Iberoamerican Workshop in Orthogonal Polynomials and Applications (EIBPOA, which stands for Encuentros Iberoamericanos de Polinomios Ortogonales y Aplicaciones, in Spanish), held at the Universidad Carlos III de Madrid, Leganés, Spain, from July 3 to July 6, 2018. These meetings were mainly focused to encourage research in the fields of approximation theory, special functions, orthogonal polynomials and their applications among graduate students as well as young researchers from Latin America, Spain and Portugal. The presentation of the state of the art as well as some recent trends constitute the aim of the lectures delivered in the EIBPOA by worldwide recognized researchers in the above fields. In this volume, several topics on the theory of polynomials orthogonal with respect to different inner products are analyzed, both from an introductory point of view for a wide spectrum of readers without an expertise in the area, as well as the emphasis on their applications in topics as integrable systems, random matrices, numerical methods in differential and partial differential equations, coding theory, and signal theory, among others.
Download or read book Orthogonal Polynomials and Special Functions written by Francisco Marcellàn and published by Springer. This book was released on 2006-10-18 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Special functions and orthogonal polynomials in particular have been around for centuries. Can you imagine mathematics without trigonometric functions, the exponential function or polynomials? The present set of lecture notes contains seven chapters about the current state of orthogonal polynomials and special functions and gives a view on open problems and future directions.
Download or read book Recent Advances in Orthogonal Polynomials Special Functions and Their Applications written by Jorge Arves and published by American Mathematical Soc.. This book was released on 2012-09-11 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the 11th International Symposium on Orthogonal Polynomials, Special Functions, and their Applications, held August 29-September 2, 2011, at the Universidad Carlos III de Madrid in Leganes, Spain. The papers cover asymptotic properties of polynomials on curves of the complex plane, universality behavior of sequences of orthogonal polynomials for large classes of measures and its application in random matrix theory, the Riemann-Hilbert approach in the study of Pade approximation and asymptotics of orthogonal polynomials, quantum walks and CMV matrices, spectral modifications of linear functionals and their effect on the associated orthogonal polynomials, bivariate orthogonal polynomials, and optimal Riesz and logarithmic energy distribution of points. The methods used include potential theory, boundary values of analytic functions, Riemann-Hilbert analysis, and the steepest descent method.
Download or read book Nonlinear Analysis and Global Optimization written by Themistocles M. Rassias and published by Springer Nature. This book was released on 2021-02-26 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume discusses aspects of nonlinear analysis in which optimization plays an important role, as well as topics which are applied to the study of optimization problems. Topics include set-valued analysis, mixed concave-convex sub-superlinear Schroedinger equation, Schroedinger equations in nonlinear optics, exponentially convex functions, optimal lot size under the occurrence of imperfect quality items, generalized equilibrium problems, artificial topologies on a relativistic spacetime, equilibrium points in the restricted three-body problem, optimization models for networks of organ transplants, network curvature measures, error analysis through energy minimization and stability problems, Ekeland variational principles in 2-local Branciari metric spaces, frictional dynamic problems, norm estimates for composite operators, operator factorization and solution of second-order nonlinear difference equations, degenerate Kirchhoff-type inclusion problems, and more.
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.
Download or read book Facta Universitatis written by and published by . This book was released on 1997 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 1574 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The J A Sampaio Martins Anniversary Volume written by António J. G. Bento and published by . This book was released on 2004 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Classical Orthogonal Polynomials of a Discrete Variable written by Arnold F. Nikiforov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: While classical orthogonal polynomials appear as solutions to hypergeometric differential equations, those of a discrete variable emerge as solutions of difference equations of hypergeometric type on lattices. The authors present a concise introduction to this theory, presenting at the same time methods of solving a large class of difference equations. They apply the theory to various problems in scientific computing, probability, queuing theory, coding and information compression. The book is an expanded and revised version of the first edition, published in Russian (Nauka 1985). Students and scientists will find a useful textbook in numerical analysis.
Download or read book Semidefinite Optimization and Convex Algebraic Geometry written by Grigoriy Blekherman and published by SIAM. This book was released on 2013-03-21 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to convex algebraic geometry and semidefinite optimization. For graduate students and researchers in mathematics and computer science.
Download or read book History of Continued Fractions and Pad Approximants written by Claude Brezinski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: The history of continued fractions is certainly one of the longest among those of mathematical concepts, since it begins with Euclid's algorithm for the great est common divisor at least three centuries B.C. As it is often the case and like Monsieur Jourdain in Moliere's "Ie bourgeois gentilhomme" (who was speak ing in prose though he did not know he was doing so), continued fractions were used for many centuries before their real discovery. The history of continued fractions and Pade approximants is also quite im portant, since they played a leading role in the development of some branches of mathematics. For example, they were the basis for the proof of the tran scendence of 11' in 1882, an open problem for more than two thousand years, and also for our modern spectral theory of operators. Actually they still are of great interest in many fields of pure and applied mathematics and in numerical analysis, where they provide computer approximations to special functions and are connected to some convergence acceleration methods. Con tinued fractions are also used in number theory, computer science, automata, electronics, etc ...
Download or read book Reviews in Numerical Analysis 1980 86 written by and published by . This book was released on 1987 with total page 872 pages. Available in PDF, EPUB and Kindle. Book excerpt: These five volumes bring together a wealth of bibliographic information in the area of numerical analysis. Containing over 17,600 reviews of articles, books, and conference proceedings, these volumes represent all the numerical analysis entries that appeared in Mathematical Reviews between 1980 and 1986. Author and key indexes appear at the end of volume 5.
