APPROXIMATING THE WEIGHT FUNCTION FOR ORTHOGONAL POLYNOMIALS ON SEVERAL INTERVALS

被引：25

作者：

GERONIMO, JS ^{[1
]}

VANASSCHE, W ^{[1
]}

机构：

[1] KATHOLIEKE UNIV LEUVEN, DEPT MATH, B-3001 HEVERLEE, BELGIUM

来源：

JOURNAL OF APPROXIMATION THEORY | 1991年 / 65卷 / 03期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1016/0021-9045(91)90096-S

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A number of methods are available to approximate the weight function for orthogonal polynomials on an interval of the real line. We present some methods to approximate weight functions for orthogonal polynomials on several intervals and give an upper bound for the error in the approximation. We introduce Turán determinants on several intervals and show that these have similar properties as in the one-interval case. These Turán determinants are useful if one deals with sieved orthogonal polynomials on one interval. The proofs depend on asymptotic properties of orthogonal polynomials with asymptotically periodic recurrence coefficients, which are of independent interest. © 1991.

引用

页码：341 / 371

页数：31

共 29 条

[1] SIEVED ULTRASPHERICAL POLYNOMIALS [J].

ALSALAM, W ;

ALLAWAY, WR ;

ASKEY, R .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1984, 284 (01) :39-55

[2]

[Anonymous], [No title captured]

[3]

APTEKAREV AI, 1986, MATH USSR SB, V53, P233

[4]

BADKOV VM, 1988, MATH NOTES+, V42, P858

[5]

BADKOV VM, 1987, MAT ZAMETKI, V42, P650

[6] ORTHOGONAL POLYNOMIALS, MEASURES AND RECURRENCE RELATIONS [J].

DOMBROWSKI, J ;

NEVAI, P .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1986, 17 (03) :752-759

[7]

GAUTSCHI W, 1990, NATO ADV SCI I C-MAT, V294, P181

[8] ORTHOGONAL POLYNOMIALS WITH ASYMPTOTICALLY PERIODIC RECURRENCE COEFFICIENTS [J].

GERONIMO, JS ;

VANASSCHE, W .

JOURNAL OF APPROXIMATION THEORY, 1986, 46 (03) :251-283

[9] ORTHOGONAL POLYNOMIALS ON SEVERAL INTERVALS VIA A POLYNOMIAL MAPPING [J].

GERONIMO, JS ;

VANASSCHE, W .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1988, 308 (02) :559-581

[10] SCATTERING-THEORY AND POLYNOMIALS ORTHOGONAL ON THE REAL LINE [J].

GERONIMO, JS ;

CASE, KM .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1980, 258 (02) :467-494

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