Asymptotics for Sobolev orthogonal polynomials with coherent pairs: The Jacobi case, type 1
Author:
K. Pan
Journal:
Proc. Amer. Math. Soc. 126 (1998), 23772388
MSC (1991):
Primary 42C05
MathSciNet review:
1443401
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Abstract: Define and as the th monic orthogonal polynomials with respect to and respectively. The pair is called a coherent pair if there exist nonzero constants such that One can divide the coherent pairs into two cases: the Jacobi case and the Laguerre case. There are two types for each case: type 1 and 2. We investigate the asymptotic properties and zero distribution of orthogonal polynomials with respect to Sobolev inner product for the coherent pair : the Jacobi case, type 1.
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 K. J. Bruinsma, M. G. de Bruin and H. G. Meijer, Zero of Sobolev orthogonal polynomials following from coherent pairs, Report of FTMI 9565, Delft University of Technology, 1995.
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 H. P. Blatt, E. B. Saff and M. Simkani, JentzschSzeg\H{o} type theorems for the zeros of best approximants, J. London Math. Soc. (2) 38 (1988) 307316. MR 90a:30004
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 H. G. Meijer, Determination of all coherent pairs of functionals, Report of FTMI 9541, Delft University of Technology, 1995.
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Additional Information
K. Pan
Affiliation:
Department of Mathematics, Barry University, Miami Shores, Florida 33161
Email:
pan@euclid.barry.edu
DOI:
http://dx.doi.org/10.1090/S0002993998043007
PII:
S 00029939(98)043007
Received by editor(s):
July 24, 1996
Received by editor(s) in revised form:
January 22, 1997
Communicated by:
J. Marshall Ash
Article copyright:
© Copyright 1998
American Mathematical Society
