On Asymptotic Properties of Polynomials which are Orthogonal on the Unit Circle, and on Certain Properties of Positive Harmonic Functions
Author: I͡A. L. Geronimus
Publisher:
Published: 1953
Total Pages: 36
ISBN-13:
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Author: I͡A. L. Geronimus
Publisher:
Published: 1953
Total Pages: 36
ISBN-13:
DOWNLOAD EBOOKAuthor: L︠A︡. L. Geronimus
Publisher:
Published: 1953
Total Pages: 29
ISBN-13:
DOWNLOAD EBOOKAuthor: Jakov L. Geronimus
Publisher:
Published: 1953
Total Pages: 29
ISBN-13:
DOWNLOAD EBOOKAuthor: Ja. L. Geronimus
Publisher:
Published: 1953
Total Pages:
ISBN-13:
DOWNLOAD EBOOKAuthor: L. Ya Geronimus
Publisher:
Published: 1953
Total Pages: 29
ISBN-13:
DOWNLOAD EBOOKAuthor: Gabor Szeg
Publisher: American Mathematical Soc.
Published: 1939-12-31
Total Pages: 448
ISBN-13: 0821810235
DOWNLOAD EBOOKThe 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: Walter Van Assche
Publisher: Springer
Published: 2006-11-14
Total Pages: 207
ISBN-13: 354047711X
DOWNLOAD EBOOKRecently 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.
Author: M. Glezerman
Publisher: American Mathematical Soc.
Published: 1962
Total Pages: 466
ISBN-13: 9780821816073
DOWNLOAD EBOOKAuthor: American Mathematical Society
Publisher: American Mathematical Soc.
Published: 1962
Total Pages: 548
ISBN-13: 9780821816028
DOWNLOAD EBOOKAuthor: N.I. Akhiezer
Publisher: SIAM
Published: 2020-12-01
Total Pages: 267
ISBN-13: 1611976383
DOWNLOAD EBOOKThe mathematical theory for many application areas depends on a deep understanding of the theory of moments. These areas include medical imaging, signal processing, computer visualization, and data science. The problem of moments has also found novel applications to areas such as control theory, image analysis, signal processing, polynomial optimization, and statistical big data. The Classical Moment Problem and Some Related Questions in Analysis presents a unified treatment of the development of the classical moment problem from the late 19th century to the middle of the 20th century. Important connections between the moment problem and many branches of analysis are presented. In this self-contained text, readers will find a unified exposition of important classical results, which are difficult to read in the original journals, as well as a strong foundation for many areas in modern applied mathematics. Researchers in areas that use techniques developed for the classical moment problem will find the book of interest.