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1.
Guillermo López Lagomasino 《Constructive Approximation》1989,5(1):199-219
Letd be a finite positive Borel measure on the interval [0, 2] such that >0 almost everywhere; andW
n be a sequence of polynomials, degW
n
=n, whose zeros (w
n
,1,,w
n,n
lie in [|z|1]. Let d
n
<> for eachnN, whered
n
=d/|W
n
(e
i
)|2. We consider the table of polynomials
n,m such that for each fixednN the system
n,m,mN, is orthonormal with respect tod
n
. If
相似文献
2.
J. Dombrowski 《Constructive Approximation》1989,5(1):371-381
Sufficient conditions are presented for the existence of an absolutely continuous part for the measure of orthogonality for a system of polynomials with unbounded recurrence coefficients. Results are obtained by analyzing the spectral measure of a related self-adjoint operator.Communicated by Paul Nevai. 相似文献
3.
Walter Van Assche 《Constructive Approximation》1989,5(1):329-345
The asymptotic behavior of thenth root of the leading coefficient of orthogonal polynomials on (–,) and the distribution of their zeros is studied for nonsymmetric weights that behave like exp(–2B|x|) whenx>0 and exp(–2Ax
) whenx<0,>0,>AB. These results generalize previous investigations of Rakhmanov and Mhaskar and Saff who handle the symmetric caseA=B.Communicated by Paul Nevai. 相似文献
4.
We obtain upper and lower bounds for Christoffel functions for Freud weights by relatively new methods, including a new way to estimate discretization of potentials. We then deduce bounds for orthogonal polynomials on thereby largely resolving a 1976 conjecture of P. Nevai. For example, let W:=e
–Q, whereQ: is even and continuous in, Q" is continuous in (0, ) andQ
'>0 in (0, ), while, for someA, B,
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