03174nam 2200613 450 99646653920331620220907173249.03-540-38857-510.1007/BFb0082413(CKB)1000000000437500(SSID)ssj0000326974(PQKBManifestationID)12061297(PQKBTitleCode)TC0000326974(PQKBWorkID)10298190(PQKB)10291613(DE-He213)978-3-540-38857-9(MiAaPQ)EBC5594889(Au-PeEL)EBL5594889(OCoLC)1076231526(MiAaPQ)EBC6842021(Au-PeEL)EBL6842021(OCoLC)793079052(PPN)155179624(EXLCZ)99100000000043750020220907d1988 uy 0engurnn|008mamaatxtccrStrong asymptotics for extremal polynomials associated with weights on R /edited by Doron S. Lubinsky, Edward B. Saff1st ed. 1988.Berlin, Germany :Springer,[1988]©19881 online resource (VIII, 156 p.) Lecture Notes in Mathematics,0075-8434 ;1305Bibliographic Level Mode of Issuance: Monograph0-387-18958-0 3-540-18958-0 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.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.Lecture Notes in Mathematics,0075-8434 ;1305Orthogonal polynomialsOrthogonal polynomials.511.66Lubinsky D. S(Doron Shaul),1955-Saff E. B.1944-MiAaPQMiAaPQMiAaPQBOOK996466539203316Strong asymptotics for extremal polynomials associated with weights on R2909892UNISA