Asymptotic behaviour of Sobolev orthogonal polynomials on the unit circle

被引：5

作者：

Castillo, Kenier ^{[1
]}

Garza, Luis E. ^{[2
]}

Marcellan, Francisco ^{[1
]}

机构：

[1] Univ Carlos III Madrid, Dept Matemat, Leganes, Spain

[2] Univ Colima, Fac Ciencias, Colima, Mexico

来源：

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2013年 / 24卷 / 01期

关键词：

probability measures on the unit circle; orthogonal polynomials; Sobolev inner products; outer relative asymptotics; zeros; 42C05; 33C47;

D O I：

10.1080/10652469.2011.649751

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this contribution, we deal with analytic properties of sequences of polynomials orthogonal with respect to a Sobolev-type inner product where mu is a non-trivial probability measure supported on the unit circle. We focus our attention on the outer relative asymptotics of these polynomials in terms of those associated with the measure mu. The behaviour of their zeros in terms of the parameter ? is studied in some illustrative examples.

引用

页码：23 / 38

页数：16

共 50 条

[1] Asymptotic behavior of Sobolev-type orthogonal polynomials on the unit circle
Moreno, AF
Marcellán, F
Pan, K
[J]. JOURNAL OF APPROXIMATION THEORY, 1999, 100 (02) : 345 - 363
[2] A family of Sobolev orthogonal polynomials on the unit circle
Berriochoa, E
Cachafeiro, A
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1999, 105 (1-2) : 163 - 173
[3] Zeros of Sobolev orthogonal polynomials on the unit circle
Castillo, K.
Garza, L. E.
Marcellan, F.
[J]. NUMERICAL ALGORITHMS, 2012, 60 (04) : 669 - 681
[4] Zeros of Sobolev orthogonal polynomials on the unit circle
K. Castillo
L. E. Garza
F. Marcellán
[J]. Numerical Algorithms, 2012, 60 : 669 - 681
[5] THE ASYMPTOTIC REPRESENTATION OF POLYNOMIALS ORTHOGONAL ON A UNIT CIRCLE
KUZMINA, AL
[J]. DOKLADY AKADEMII NAUK SSSR, 1956, 107 (06): : 793 - 795
[6] ASYMPTOTIC PROPERTIES OF ORTHOGONAL POLYNOMIALS ON UNIT CIRCLE
FANTA, K
[J]. PERIODICA POLYTECHNICA-ELECTRICAL ENGINEERING, 1972, 16 (01): : 33 - &
[7] ORTHOGONAL POLYNOMIALS OF SOBOLEV TYPE ON THE UNIT-CIRCLE
CACHAFEIRO, A
MARCELLAN, F
[J]. JOURNAL OF APPROXIMATION THEORY, 1994, 78 (01) : 127 - 146
[8] Sobolev-type orthogonal polynomials on the unit circle
Marcellán, F
Moral, L
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2002, 128 (2-3) : 329 - 363
[9] Asymptotic behaviour of orthogonal polynomials on the unit circle with asymptotically periodic reflection coefficients
Peherstorfer, F
Steinbauer, R
[J]. JOURNAL OF APPROXIMATION THEORY, 1997, 88 (03) : 316 - 353
[10] AN ASYMPTOTIC FORMULA FOR DERIVATIVES OF ORTHOGONAL POLYNOMIALS ON UNIT CIRCLE
HORUP, C
[J]. MATHEMATICA SCANDINAVICA, 1967, 20 (01) : 32 - &

← 1 2 3 4 5 →