Download or read book Asymptotic Properties of Polynomials with Auxiliary Conditions of Interpolation written by Joseph Leonard Walsh and published by . This book was released on 1961 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let a closed bounded point set E be given in the z-plane. Necessary and sufficient conditions are found for validity of the following: given assigned conditions of interpolation in a finite number of points: pn(zk) = Ank; there exists a sequence of polynomials pn(z) satisfying these conditions and lim sup max pn(z), z on E 1/n = (E), where (E) is the transfinite diameter of E. (Author).
Download or read book On the Asymptotic Properties of Extremal Polynomials with Prescribed Constant Term written by J. L. Walsh and published by . This book was released on 1960 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Discrete Orthogonal Polynomials AM 164 written by J. Baik and published by Princeton University Press. This book was released on 2007-01-02 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the theory and applications of discrete orthogonal polynomials--polynomials that are orthogonal on a finite set. Unlike other books, Discrete Orthogonal Polynomials addresses completely general weight functions and presents a new methodology for handling the discrete weights case. J. Baik, T. Kriecherbauer, K. T.-R. McLaughlin & P. D. Miller focus on asymptotic aspects of general, nonclassical discrete orthogonal polynomials and set out applications of current interest. Topics covered include the probability theory of discrete orthogonal polynomial ensembles and the continuum limit of the Toda lattice. The primary concern throughout is the asymptotic behavior of discrete orthogonal polynomials for general, nonclassical measures, in the joint limit where the degree increases as some fraction of the total number of points of collocation. The book formulates the orthogonality conditions defining these polynomials as a kind of Riemann-Hilbert problem and then generalizes the steepest descent method for such a problem to carry out the necessary asymptotic analysis.
Download or read book Bounds and Asymptotics for Orthogonal Polynomials for Varying Weights written by Eli Levin and published by Springer. This book was released on 2018-02-13 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book establishes bounds and asymptotics under almost minimal conditions on the varying weights, and applies them to universality limits and entropy integrals. Orthogonal polynomials associated with varying weights play a key role in analyzing random matrices and other topics. This book will be of use to a wide community of mathematicians, physicists, and statisticians dealing with techniques of potential theory, orthogonal polynomials, approximation theory, as well as random matrices.
Download or read book Asymptotics for Orthogonal Polynomials written by Walter Van Assche and published by Springer. This book was released on 2006-11-14 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently there has been a great deal of interest in the theory of orthogonal polynomials. The number of books treating the subject, however, is limited. This monograph brings together some results involving the asymptotic behaviour of orthogonal polynomials when the degree tends to infinity, assuming only a basic knowledge of real and complex analysis. An extensive treatment, starting with special knowledge of the orthogonality measure, is given for orthogonal polynomials on a compact set and on an unbounded set. Another possible approach is to start from properties of the coefficients in the three-term recurrence relation for orthogonal polynomials. This is done using the methods of (discrete) scattering theory. A new method, based on limit theorems in probability theory, to obtain asymptotic formulas for some polynomials is also given. Various consequences of all the results are described and applications are given ranging from random matrices and birth-death processes to discrete Schrödinger operators, illustrating the close interaction with different branches of applied mathematics.
Download or read book Technical Abstract Bulletin written by Defense Documentation Center (U.S.) and published by . This book was released on 1961-07 with total page 1766 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book U S Government Research Reports written by and published by . This book was released on 1961 with total page 1216 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Asymptotic Properties of Polynomials which are Orthogonal on the Unit Circle and on Certain Properties of Positive Harmonic Functions written by I͡A. L. Geronimus and published by . This book was released on 1953 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometry of Polynomials written by Morris Marden and published by American Mathematical Soc.. This book was released on 1949-12-31 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the years since the first edition of this well-known monograph appeared, the subject (the geometry of the zeros of a complex polynomial) has continued to display the same outstanding vitality as it did in the first 150 years of its history, beginning with the contributions of Cauchy and Gauss. Thus, the number of entries in the bibliography of this edition had to be increased from about 300 to about 600 and the book enlarged by one third. It now includes a more extensive treatment of Hurwitz polynomials and other topics. The new material on infrapolynomials, abstract polynomials, and matrix methods is of particular interest.
Download or read book Approximation in the Sense of Least P th Powers by Polynomials with Auxiliary Conditions of Interpolation written by Abraham Spitzbart and published by . This book was released on 1940 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Annales Polonici mathematici written by and published by . This book was released on 1962 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Strong Asymptotics for Extremal Polynomials Associated with Weights on R written by Doron Shaul Lubinsky and published by Lecture Notes in Mathematics. This book was released on 1988-03-09 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: 0. The results are consequences of a strengthened form of the following assertion: Given 0 > 1. Auxiliary results include inequalities for weighted polynomials, and zeros of extremal polynomials. The monograph is fairly self-contained, with proofs involving elementary complex analysis, and the theory of orthogonal and extremal polynomials. It should be of interest to research workers in approximation theory and orthogonal polynomials.
Download or read book Interpolation and Approximation by Rational Functions in the Complex Domain written by J. L. Walsh and published by American Mathematical Soc.. This book was released on 1935-12-31 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present work is restricted to the representation of functions in the complex domain, particularly analytic functions, by sequences of polynomials or of more general rational functions whose poles are preassigned, the sequences being defined either by interpolation or by extremal properties (i.e. best approximation). Taylor's series plays a central role in this entire study, for it has properties of both interpolation and best approximation, and serves as a guide throughout the whole treatise. Indeed, almost every result given on the representation of functions is concerned with a generalization either of Taylor's series or of some property of Taylor's series--the title ``Generalizations of Taylor's Series'' would be appropriate.
Download or read book Polynomials in Several Non commuting Variables and Some of Their Asymptotic Properties written by Moe Barakat and published by . This book was released on 2004 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Topics in Polynomial and Rational Interpolation and Approximation written by Richard S. Varga and published by . This book was released on 1982 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bulletin of the American Mathematical Society written by and published by . This book was released on 1975 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On asymptotic properties of polynomials which are orthogonal on the unit circle and on certain properties written by Jakov L. Geronimus and published by . This book was released on 1953 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:
