Orthogonal Polynomials Of Several Variables Second Edition
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| Author | : Charles F. Dunkl |
| Publisher | : Cambridge University Press |
| Total Pages | : 439 |
| Release | : 2014-08-21 |
| Genre | : Mathematics |
| ISBN | : 1316061906 |
Serving both as an introduction to the subject and as a reference, this book presents the theory in elegant form and with modern concepts and notation. It covers the general theory and emphasizes the classical types of orthogonal polynomials whose weight functions are supported on standard domains. The approach is a blend of classical analysis and symmetry group theoretic methods. Finite reflection groups are used to motivate and classify symmetries of weight functions and the associated polynomials. This revised edition has been updated throughout to reflect recent developments in the field. It contains 25% new material, including two brand new chapters on orthogonal polynomials in two variables, which will be especially useful for applications, and orthogonal polynomials on the unit sphere. The most modern and complete treatment of the subject available, it will be useful to a wide audience of mathematicians and applied scientists, including physicists, chemists and engineers.
| Author | : Charles F. Dunkl |
| Publisher | : Cambridge University Press |
| Total Pages | : 439 |
| Release | : 2014-08-21 |
| Genre | : Mathematics |
| ISBN | : 1107071895 |
Updated throughout, this revised edition contains 25% new material covering progress made in the field over the past decade.
| Author | : Themistocles M. Rassias |
| Publisher | : World Scientific |
| Total Pages | : 658 |
| Release | : 1993 |
| Genre | : Mathematics |
| ISBN | : 9789810206147 |
This volume presents an account of some of the most important work that has been done on various research problems in the theory of polynomials of one and several variables and their applications. It is dedicated to P L Chebyshev, a leading Russian mathematician.
| Author | : Gabor Szeg |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 448 |
| Release | : 1939-12-31 |
| Genre | : Mathematics |
| ISBN | : 0821810235 |
The general theory of orthogonal polynomials was developed in the late 19th century from a study of continued fractions by P. L. Chebyshev, even though special cases were introduced earlier by Legendre, Hermite, Jacobi, Laguerre, and Chebyshev himself. It was further developed by A. A. Markov, T. J. Stieltjes, and many other mathematicians. The book by Szego, originally published in 1939, is the first monograph devoted to the theory of orthogonal polynomials and its applications in many areas, including analysis, differential equations, probability and mathematical physics. Even after all the years that have passed since the book first appeared, and with many other books on the subject published since then, this classic monograph by Szego remains an indispensable resource both as a textbook and as a reference book. It can be recommended to anyone who wants to be acquainted with this central topic of mathematical analysis.
| Author | : Valérie Berthé |
| Publisher | : Cambridge University Press |
| Total Pages | : 496 |
| Release | : 2016-02-26 |
| Genre | : Mathematics |
| ISBN | : 1316462528 |
Internationally recognised researchers look at developing trends in combinatorics with applications in the study of words and in symbolic dynamics. They explain the important concepts, providing a clear exposition of some recent results, and emphasise the emerging connections between these different fields. Topics include combinatorics on words, pattern avoidance, graph theory, tilings and theory of computation, multidimensional subshifts, discrete dynamical systems, ergodic theory, numeration systems, dynamical arithmetics, automata theory and synchronised words, analytic combinatorics, continued fractions and probabilistic models. Each topic is presented in a way that links it to the main themes, but then they are also extended to repetitions in words, similarity relations, cellular automata, friezes and Dynkin diagrams. The book will appeal to graduate students, research mathematicians and computer scientists working in combinatorics, theory of computation, number theory, symbolic dynamics, tilings and stringology. It will also interest biologists using text algorithms.
| Author | : Giovanni Molica Bisci |
| Publisher | : Cambridge University Press |
| Total Pages | : 401 |
| Release | : 2016-03-11 |
| Genre | : Mathematics |
| ISBN | : 1107111943 |
A thorough graduate-level introduction to the variational analysis of nonlinear problems described by nonlocal operators.
| Author | : Grzegorz Tomkowicz |
| Publisher | : Cambridge University Press |
| Total Pages | : 367 |
| Release | : 2016-06-14 |
| Genre | : Mathematics |
| ISBN | : 1107042593 |
The Banach-Tarski Paradox seems patently false. The authors explain it and its implications in terms appropriate for an undergraduate.
| Author | : Marcelo Aguiar |
| Publisher | : Cambridge University Press |
| Total Pages | : 897 |
| Release | : 2022-10-31 |
| Genre | : Mathematics |
| ISBN | : 100924373X |
The goal of this monograph is to develop Hopf theory in the setting of a real reflection arrangement. The central notion is that of a Coxeter bialgebra which generalizes the classical notion of a connected graded Hopf algebra. The authors also introduce the more structured notion of a Coxeter bimonoid and connect the two notions via a family of functors called Fock functors. These generalize similar functors connecting Hopf monoids in the category of Joyal species and connected graded Hopf algebras. This monograph opens a new chapter in Coxeter theory as well as in Hopf theory, connecting the two. It also relates fruitfully to many other areas of mathematics such as discrete geometry, semigroup theory, associative algebras, algebraic Lie theory, operads, and category theory. It is carefully written, with effective use of tables, diagrams, pictures, and summaries. It will be of interest to students and researchers alike.
| Author | : Andries E. Brouwer |
| Publisher | : |
| Total Pages | : 481 |
| Release | : 2022-01-13 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 1316512037 |
This monograph on strongly regular graphs is an invaluable reference for anybody working in algebraic combinatorics.
| Author | : Damir Z. Arov |
| Publisher | : Cambridge University Press |
| Total Pages | : 1050 |
| Release | : 2022-05-26 |
| Genre | : Mathematics |
| ISBN | : 1009021737 |
The authors explain in this work a new approach to observing and controlling linear systems whose inputs and outputs are not fixed in advance. They cover a class of linear time-invariant state/signal system that is general enough to include most of the standard classes of linear time-invariant dynamical systems, but simple enough that it is easy to understand the fundamental principles. They begin by explaining the basic theory of finite-dimensional and bounded systems in a way suitable for graduate courses in systems theory and control. They then proceed to the more advanced infinite-dimensional setting, opening up new ways for researchers to study distributed parameter systems, including linear port-Hamiltonian systems and boundary triplets. They include the general non-passive part of the theory in continuous and discrete time, and provide a short introduction to the passive situation. Numerous examples from circuit theory are used to illustrate the theory.
