LEADER 02773nam 2200589 450 001 996466375003316 005 20220820094033.0 010 $a3-540-48323-3 024 7 $a10.1007/BFb0076133 035 $a(CKB)1000000000437169 035 $a(SSID)ssj0000327626 035 $a(PQKBManifestationID)12083611 035 $a(PQKBTitleCode)TC0000327626 035 $a(PQKBWorkID)10303703 035 $a(PQKB)11783380 035 $a(DE-He213)978-3-540-48323-6 035 $a(MiAaPQ)EBC5579035 035 $a(Au-PeEL)EBL5579035 035 $a(OCoLC)1066181872 035 $a(MiAaPQ)EBC6819216 035 $a(Au-PeEL)EBL6819216 035 $a(OCoLC)793079352 035 $a(PPN)155204629 035 $a(EXLCZ)991000000000437169 100 $a20220820d1994 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aWeighted approximation with varying weight /$fVilmos Totik 205 $a1st ed. 1994. 210 1$aBerlin ;$aHeidelberg :$cSpringer-Verlag,$d[1994] 210 4$dİ1994 215 $a1 online resource (VI, 118 p.) 225 1 $aLecture Notes in Mathematics ;$vVolume 1569 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-57705-X 327 $aFreud weights -- Approximation with general weights -- Varying weights -- Applications. 330 $aA new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$vVolume 1569. 606 $aApproximation theory 615 0$aApproximation theory. 676 $a511.4 700 $aTotik$b V.$01185534 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466375003316 996 $aWeighted approximation with varying weight$92906393 997 $aUNISA