000 02928nam a22004815i 4500
001 978-3-540-38857-9
003 DE-He213
005 20160624101811.0
007 cr nn 008mamaa
008 121227s1988 gw | s |||| 0|eng d
020 _a9783540388579
_9978-3-540-38857-9
024 7 _a10.1007/BFb0082413
_2doi
050 4 _aQA297-299.4
072 7 _aPBKS
_2bicssc
072 7 _aMAT021000
_2bisacsh
072 7 _aMAT006000
_2bisacsh
082 0 4 _a518
_223
100 1 _aLubinsky, Doron S.
_eauthor.
245 1 0 _aStrong Asymptotics for Extremal Polynomials Associated with Weights on ℝ
_h[electronic resource] /
_cby Doron S. Lubinsky, Edward B. Saff.
260 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c1988.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c1988.
300 _aVIII, 156 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1305
505 0 _aNotation 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.
520 _a0. 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.
650 0 _aMathematics.
650 0 _aNumerical analysis.
650 1 4 _aMathematics.
650 2 4 _aNumerical Analysis.
700 1 _aSaff, Edward B.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540189589
786 _dSpringer
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1305
856 4 0 _uhttp://dx.doi.org/10.1007/BFb0082413
942 _2EBK923
_cEBK
999 _c30217
_d30217