ORTHOGONAL EXPANSIONS AND THE ERROR OF WEIGHTED POLYNOMIAL-APPROXIMATION FOR ERDOS WEIGHTS

被引：5

作者：

LUBINSKY, DS ^{[1
]}

MTHEMBU, TZ ^{[1
]}

机构：

[1] UNIV WITWATERSRAND,DEPT MATH,WITWATERSRAND 2050,SOUTH AFRICA

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 1992年 / 13卷 / 3-4期

关键词：

ORTHOGONAL EXPANSIONS; (C; 1); BOUNDS; BOHR-TYPE INEQUALITIES; ERROR OF APPROXIMATION; JACKSON-FAVARD INEQUALITIES; ERDOS WEIGHTS;

D O I：

10.1080/01630569208816481

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Some (C, 1) bounds for orthogonal expansions associated with Erdos weights are established. Roughly speaking, Erdos weights are weights of the form W := e(-Q), where Q is even, continuous and has faster than polynomial growth at infinity. Typical examples are W(x) := exp(-exp(absolute value of x(alpha))), alpha > 1 or W(x) := exp(-exp(exp(absolute value of x(alpha)))), alpha > 1, and so on. We shall use these bounds together with Bohr-type inequalities, to establish L(p), 1 less-than-or-equal-to p less-than-or-equal-to infinity, Jackson-Favard inequalities.

引用

页码：327 / 347

页数：21

共 50 条

[1] WEIGHTED POLYNOMIAL-APPROXIMATION WITH FREUD WEIGHTS
LUBINSKY, DS
TOTIK, V
[J]. CONSTRUCTIVE APPROXIMATION, 1994, 10 (03) : 301 - 315
[2] EXTREMAL ORTHOGONAL MEASURES FOR WEIGHTED POLYNOMIAL-APPROXIMATION
KOOSIS, P
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1990, 311 (09): : 503 - 506
[3] BEST WEIGHTED POLYNOMIAL-APPROXIMATION VIA JACOBI-EXPANSIONS
LUBINSKY, DS
TOTIK, V
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1994, 25 (02) : 555 - 570
[4] WEIGHTED POLYNOMIAL-APPROXIMATION
BRENNAN, J
[J]. LECTURE NOTES IN MATHEMATICS, 1984, 1043 : 461 - 465
[5] WEIGHTED POLYNOMIAL-APPROXIMATION
MHASKAR, HN
[J]. JOURNAL OF APPROXIMATION THEORY, 1986, 46 (01) : 100 - 110
[6] ANALOGS OF FREUD CONJECTURE FOR ERDOS TYPE WEIGHTS AND RELATED POLYNOMIAL-APPROXIMATION PROBLEMS
KNOPFMACHER, A
LUBINSKY, DS
[J]. LECTURE NOTES IN MATHEMATICS, 1987, 1287 : 21 - 69
[7] POLYNOMIAL-APPROXIMATION WITH EXPONENTIAL WEIGHTS
DITZIAN, Z
LUBINSKY, DS
NEVAI, P
TOTIK, V
[J]. ACTA MATHEMATICA HUNGARICA, 1987, 50 (1-2) : 165 - 175
[8] WEIGHTED POLYNOMIAL-APPROXIMATION ON THE REAL LINE
KROO, A
SZABADOS, J
[J]. JOURNAL OF APPROXIMATION THEORY, 1995, 83 (01) : 41 - 64
[9] WEIGHTED POLYNOMIAL-APPROXIMATION ON UNBOUNDED INTERVALS
ZALIK, RA
[J]. JOURNAL OF APPROXIMATION THEORY, 1980, 28 (02) : 113 - 119
[10] QUASI-ANALYTICITY AND WEIGHTED POLYNOMIAL-APPROXIMATION
ZAPATA, GI
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1984, 298 (14): : 317 - 319

← 1 2 3 4 5 →