Geronimus transformations of bivariate linear functionals

被引：0

作者：

Marcellan, Francisco ^{[1
]}

Marriaga, Misael E. ^{[2
]}

Perez, Teresa E. ^{[3
,4
]}

Pinar, Miguel A. ^{[3
,4
]}

机构：

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

[2] Univ Rey Juan Carlos, Dept Matemat Aplicada Ciencia & Ingn Mat & Tecnol, Mostoles, Spain

[3] Univ Granada, Fac Ciencias, Inst Matemat IEMath GR, Granada, Spain

[4] Univ Granada, Fac Ciencias, Dept Matemat Aplicada, Granada, Spain

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2020年 / 484卷 / 02期

关键词：

Bivariate orthogonal polynomials; Classical and semiclassical orthogonal polynomials; ORTHOGONAL POLYNOMIALS; INVERSE PROBLEM; PRODUCT; FORM;

D O I：

10.1016/j.jmaa.2019.123736

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given a linear functional u in the linear space of polynomials in two variables with real coefficients and a polynomial lambda(x, y), in this contribution we deal with Geronimus transformations of u, i.e., those linear functionals v such that u = lambda(x, y)v. The connection formulas between the sequences of bivariate orthogonal polynomials with respect to u and v are given. A matrix interpretation of such transformations by using LU and UL factorizations of the block Jacobi matrices associated with such polynomials is given. Finally, some illustrative examples of Geronimus transformations of weight function supported in domains of R-2 are discussed. (C) 2019 Elsevier Inc. All rights reserved.

引用

页数：30

共 50 条

[1] Multiple Geronimus transformations
Derevyagin, M.
Garcia-Ardila, J. C.
Marcellan, F.
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2014, 454 : 158 - 183
[2] Bivariate Polynomial Interpolation at the Geronimus Nodes
Harris, Lawrence A.
[J]. COMPLEX ANALYSIS AND DYNAMICAL SYSTEMS V, 2013, 591 : 135 - 147
[3] BIVARIATE SPLINE FUNCTIONS AND APPROXIMATION OF LINEAR FUNCTIONALS
NIELSON, GM
[J]. NUMERISCHE MATHEMATIK, 1973, 21 (02) : 138 - 160
[4] Spectral transformations of hermitian linear functionals
Cantero, M. J.
Moral, L.
Velazquez, L.
[J]. RECENT ADVANCES IN ORTHOGONAL POLYNOMIALS, SPECIAL FUNCTIONS, AND THEIR APPLICATIONS, 2011, 578 : 63 - 82
[5] OPTIMAL APPROXIMATION OF LINEAR FUNCTIONALS IN SPACES OF BIVARIATE FUNCTIONS
MANSFIELD, LE
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1971, 8 (01) : 115 - +
[6] On rational transformations of linear functionals:: direct problem
Alfaro, M
Marcellán, F
Peña, A
Rezola, ML
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 298 (01) : 171 - 183
[7] On efficient estimation of linear functionals of a bivariate distribution with known marginals
Peng, HX
Schick, A
[J]. STATISTICS & PROBABILITY LETTERS, 2002, 59 (01) : 83 - 91
[8] LINEAR FUNCTIONALS INVARIANT UNDER MEASURE PRESERVING TRANSFORMATIONS
KWAPIEN, S
[J]. MATHEMATISCHE NACHRICHTEN, 1984, 119 : 175 - 179
[9] Spectral Transformations and Associated Linear Functionals of the First Kind
Garcia-Ardila, Juan Carlos
Marcellan, Francisco
[J]. AXIOMS, 2021, 10 (02)
[10] Nonparametric estimation of linear functionals of a bivariate distribution under univariate censoring
Lu, Xuewen
Burke, M. D.
[J]. JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2008, 138 (10) : 3238 - 3256

← 1 2 3 4 5 →