02773nam 2200589 450 99646637500331620220820094033.03-540-48323-310.1007/BFb0076133(CKB)1000000000437169(SSID)ssj0000327626(PQKBManifestationID)12083611(PQKBTitleCode)TC0000327626(PQKBWorkID)10303703(PQKB)11783380(DE-He213)978-3-540-48323-6(MiAaPQ)EBC5579035(Au-PeEL)EBL5579035(OCoLC)1066181872(MiAaPQ)EBC6819216(Au-PeEL)EBL6819216(OCoLC)793079352(PPN)155204629(EXLCZ)99100000000043716920220820d1994 uy 0engurnn|008mamaatxtccrWeighted approximation with varying weight /Vilmos Totik1st ed. 1994.Berlin ;Heidelberg :Springer-Verlag,[1994]©19941 online resource (VI, 118 p.) Lecture Notes in Mathematics ;Volume 1569Bibliographic Level Mode of Issuance: Monograph3-540-57705-X Freud weights -- Approximation with general weights -- Varying weights -- Applications.A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.Lecture notes in mathematics (Springer-Verlag) ;Volume 1569.Approximation theoryApproximation theory.511.4Totik V.1185534MiAaPQMiAaPQMiAaPQBOOK996466375003316Weighted approximation with varying weight2906393UNISA