Krall-type orthogonal polynomials in several variables

被引：15

作者：

Fernandez, Lidia ^{[1
,2
]}

Perez, Teresa E. ^{[1
,2
]}

Pinar, Miguel A. ^{[1
,2
]}

Xu, Yuan ^{[3
]}

机构：

[1] Univ Granada, Dept Matemat Aplicada, E-18071 Granada, Spain

[2] Univ Granada, Inst Carlos Fis Teor & Computac 1, E-18071 Granada, Spain

[3] Univ Oregon, Dept Math, Eugene, OR 97403 USA

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2010年 / 233卷 / 06期

关键词：

Orthogonal polynomials in several variables; Krall-type orthogonal polynomials; Reproducing kernel; WEIGHT;

D O I：

10.1016/j.cam.2009.02.067

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a bilinear form obtained by adding a Dirac mass to a positive definite moment functional defined in the linear space of polynomials in several variables, explicit formulas of orthogonal polynomials are derived from the orthogonal polynomials associated with the moment functional. Explicit formula for the reproducing kernel is also derived and used to establish certain inequalities for classical orthogonal polynomials. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：1519 / 1524

页数：6

共 41 条

[21] Asymptotics of Orthogonal Polynomials for a Weight with a Jump on [−1,1]
A. Foulquié Moreno
A. Martínez-Finkelshtein
V. L. Sousa
Constructive Approximation, 2011, 33 : 219 - 263
[22] Asymptotics of Orthogonal Polynomials for a Weight with a Jump on [-1,1]
Foulquie Moreno, A.
Martinez-Finkelshtein, A.
Sousa, V. L.
CONSTRUCTIVE APPROXIMATION, 2011, 33 (02) : 219 - 263
[23] ORTHOGONAL POLYNOMIALS ARISING IN CONNECTION WITH HANKEL FORMS OF HIGHER WEIGHT
PEETRE, J
BULLETIN DES SCIENCES MATHEMATIQUES, 1992, 116 (02): : 265 - 284
[24] Muckenhoupt inequality with three measures and applications to Sobolev orthogonal polynomials
Colorado, E.
Pestana, D.
Rodriguez, J. M.
Romera, E.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 407 (02) : 369 - 386
[25] Sobolev Spaces with Respect to Measures in Curves and Zeros of Sobolev Orthogonal Polynomials
Rodriguez, Jose M.
Sigarreta, Jose M.
ACTA APPLICANDAE MATHEMATICAE, 2008, 104 (03) : 325 - 353
[26] Asymptotic Behavior and Zero Distribution of Polynomials Orthogonal with Respect to Bessel Functions
Deano, Alfredo
Kuijlaars, Arno B. J.
Roman, Pablo
CONSTRUCTIVE APPROXIMATION, 2016, 43 (01) : 153 - 196
[27] Sobolev Spaces with Respect to Measures in Curves and Zeros of Sobolev Orthogonal Polynomials
Jose M. Rodriguez
Jose M. Sigarreta
Acta Applicandae Mathematicae, 2008, 104
[28] ORTHOGONAL POLYNOMIALS WITH PERIODICALLY MODULATED RECURRENCE COEFFICIENTS IN THE JORDAN BLOCK CASE
Swiderski, Grzegorz
Trojan, Bartosz
ANNALES DE L INSTITUT FOURIER, 2024, 74 (03) : 1521 - 1601
[29] ALGEBRO-GEOMETRIC ASPECTS OF THE CHRISTOFFEL-DARBOUX KERNELS FOR CLASSICAL ORTHOGONAL POLYNOMIALS
Sawa, Masanori
Uchida, Yukihiro
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2020, 373 (02) : 1243 - 1264
[30] Orthogonal Polynomials on the Circle for the Weight w Satisfying Conditions w, w-1 ε BMO
Denisov, Sergey
Rush, Keith
CONSTRUCTIVE APPROXIMATION, 2017, 46 (02) : 285 - 303

← 1 2 3 4 5 →