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Polynomials Orthogonal over a Region and Bieberbach Polynomials

Author: Pavel Kondratʹevich Suetin
Publisher: American Mathematical Soc.
ISBN: 9780821830000
Category : Mathematics
Languages : en
Pages : 100

Book Description
Discusses orthogonal polynomials.

Polynomials Orthogonal over a Region and Bieberbach Polynomials

Author: Pavel Kondratʹevich Suetin
Publisher: American Mathematical Soc.
ISBN: 9780821830000
Category : Mathematics
Languages : en
Pages : 100

Book Description
Discusses orthogonal polynomials.

Orthogonal Polynomials

Author: Paul Nevai
Publisher: Springer Science & Business Media
ISBN: 9400905017
Category : Mathematics
Languages : en
Pages : 472

Book Description
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 in Two Variables

Author: P. K. Suetin
Publisher: CRC Press
ISBN: 9789056991678
Category : Mathematics
Languages : en
Pages : 494

Book Description
Presenting a comprehensive theory of orthogonal polynomials in two real variables and properties of Fourier series in these polynomials, this volume also gives cases of orthogonality over a region and on a contour. The text includes the classification of differential equations which admits orthogonal polynomials as eigenfunctions and several two-dimensional analogies of classical orthogonal polynomials.

Discrepancy of Signed Measures and Polynomial Approximation

Author: Vladimir V. Andrievskii
Publisher: Springer Science & Business Media
ISBN: 1475749996
Category : Mathematics
Languages : en
Pages : 444

Book Description
A concise outline of the basic facts of potential theory and quasiconformal mappings makes this book an ideal introduction for non-experts who want to get an idea of applications of potential theory and geometric function theory in various fields of construction analysis.

Lectures on Complex Approximation

Author: GAIER
Publisher: Springer Science & Business Media
ISBN: 1461248140
Category : Mathematics
Languages : en
Pages : 207

Book Description
The theory of General Relativity, after its invention by Albert Einstein, remained for many years a monument of mathemati cal speculation, striking in its ambition and its formal beauty, but quite separated from the main stream of modern Physics, which had centered, after the early twenties, on quantum mechanics and its applications. In the last ten or fifteen years, however, the situation has changed radically. First, a great deal of significant exper~en tal data became available. Then important contributions were made to the incorporation of general relativity into the framework of quantum theory. Finally, in the last three years, exciting devel opments took place which have placed general relativity, and all the concepts behind it, at the center of our understanding of par ticle physics and quantum field theory. Firstly, this is due to the fact that general relativity is really the "original non-abe lian gauge theory," and that our description of quantum field in teractions makes extensive use of the concept of gauge invariance. Secondly, the ideas of supersymmetry have enabled theoreticians to combine gravity with other elementary particle interactions, and to construct what is perhaps the first approach to a more finite quantum theory of gravitation, which is known as super gravity.

Orthogonal Polynomials and Special Functions

Author: Richard Askey
Publisher: SIAM
ISBN: 0898710189
Category : Mathematics
Languages : en
Pages : 115

Book Description
This volume presents the idea that one studies orthogonal polynomials and special functions to use them to solve problems.

Encyclopaedia of Mathematics

Author: Michiel Hazewinkel
Publisher: Springer Science & Business Media
ISBN: 9401512396
Category : Mathematics
Languages : en
Pages : 496

Book Description
This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathema tics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclo paedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977 - 1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivision has been used). The main requirement for these articles has been that they should give a reason ably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of pre cise theorems with detailed definitions and technical details on how to carry out proofs and con structions.