Sharp estimates for Jacobi matrices and chain sequences, II

被引：2

作者：

Szwarc, R

机构：

[1] Univ Wroclaw, Inst Math, PL-50384 Wroclaw, Poland

[2] Polish Acad Sci, Inst Math, PL-00950 Warsaw, Poland

来源：

JOURNAL OF APPROXIMATION THEORY | 2003年 / 125卷 / 02期

关键词：

orthogonal polynomials; chain sequences; Jacobi matrices; recurrence relation;

D O I：

10.1016/j.jat.2003.11.006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Chain sequences are positive sequences{c(n)} of the form c(n) = g(n)(1 - g(n-1)) for a nonnegative sequence {g(n)}. They are very useful in estimating the norms of Jacobi matrices and for localizing the interval of orthogonality for orthogonal polynomials. We give optimal estimates for the chain sequences which are more precise than the ones obtained in the paper (Constructive Approx. 6 (1990) 363) and in our earlier paper (J. Approx. Theory 118 (2002) 94). (C) 2003 Published by Elsevier Inc.

引用

页码：295 / 302

页数：8

共 8 条

[1] [Anonymous], 1962, T AM MATH SOC
[2] [Anonymous], 1948, ANAL THEORY CONTINUE
[3] CHIHARA T, 1982, T AM MATH SOC, V170, P623
[4] Chihara T.S., 1978, MATH ITS APPL, V13
[5] ON THE CONVERGENCE OF LIMIT PERIODIC CONTINUED FRACTIONS K(AN/1), WHERE AN-]-1/4 .3.
JACOBSEN, L
MASSON, DR
[J]. CONSTRUCTIVE APPROXIMATION, 1990, 6 (04) : 363 - 374
[6] CHAIN SEQUENCES AND COMPACT PERTURBATIONS OF ORTHOGONAL POLYNOMIALS
SZWARC, R
[J]. MATHEMATISCHE ZEITSCHRIFT, 1994, 217 (01) : 57 - 71
[7] Chain sequences, orthogonal polynomials, and Jacobi matrices
Szwarc, R
[J]. JOURNAL OF APPROXIMATION THEORY, 1998, 92 (01) : 59 - 73
[8] Sharp estimates for Jacobi matrices and chain sequences
Szwarc, R
[J]. JOURNAL OF APPROXIMATION THEORY, 2002, 118 (01) : 94 - 105

← 1 →