Asymptotic Properties of Polynomials with Auxiliary Conditions of Interpolation
Asymptotic Properties of Polynomials with Auxiliary Conditions of Interpolation

Author: Joseph Leonard Walsh

Publisher:

Published: 1961

Total Pages: 34

ISBN-13:

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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).

Strong Asymptotics for Extremal Polynomials Associated with Weights on R
Strong Asymptotics for Extremal Polynomials Associated with Weights on R

Author: Doron Shaul Lubinsky

Publisher: Lecture Notes in Mathematics

Published: 1988-03-09

Total Pages: 170

ISBN-13:

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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.

AFOSR.
AFOSR.

Author: United States. Air Force. Office of Scientific Research

Publisher:

Published: 1959

Total Pages: 718

ISBN-13:

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Geometry of Polynomials
Geometry of Polynomials

Author: Morris Marden

Publisher: American Mathematical Soc.

Published: 1949-12-31

Total Pages: 260

ISBN-13: 0821815032

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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.