Strong asymptotics for extremal polynomials associated with weights on R / / edited by Doron S. Lubinsky, Edward B. Saff

• Pubblicazione: Berlin, Germany : , : Springer, , [1988]; ©1988
• Edizione: 1st ed. 1988.
• Descrizione fisica: 1 online resource (VIII, 156 p.)
• Disciplina: 511.66
• Soggetto topico: Orthogonal polynomials
• Persona (resp. second.): LubinskyD. S <1955-> (Doron Shaul); SaffE. B. <1944->
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di contenuto: Notation and index of notation -- Statement of main results -- Weighted polynomials and zeros of extremal polynomials -- Integral equations -- Polynomial approximation of potentials -- Infinite-finite range inequalities and their sharpness -- The largest zeros of extremal polynomials -- Further properties of Un, R(x) -- Nth root asymptotics for extremal polynomials -- Approximation by certain weighted polynomials, I -- Approximation by certain weighted polynomials, II -- Bernstein's formula and bernstein extremal polynomials -- Proof of the asymptotics for Enp(W) -- Proof of the asymptotics for the Lp extremal polynomials -- The case p=2 : Orthonormal polynomials.
• Sommario/riassunto: 0. The results are consequences of a strengthened form of the following assertion: Given 0 <p<, f Lp ( ) and a certain sequence of positive numbers associated with Q(x), there exist polynomials Pn of degree at most n, n = 1,2,3..., such that if and only if f(x) = 0 for a.e. 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.
• Titolo autorizzato: Strong asymptotics for extremal polynomials associated with weights on R
• ISBN: 3-540-38857-5
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 996466539203316
• Lo trovi qui: Univ. di Salerno
• Serie: Lecture Notes in Mathematics, . 0075-8434 ; ; 1305