Linear Combinations of d-Orthogonal Polynomials

被引：5
|
作者：
Marcellan, Francisco [1 ,2 ]
Saib, Abdessadek [3 ]
机构：
[1] Univ Carlos III Madrid, Dept Matemat, Leganes 28911, Spain
[2] Inst Ciencias Matemat ICMAT, Campus Cantoblanco, Madrid 28049, Spain
[3] Univ Tebessa, Dept Math, Tebessa 12002, Algeria
来源：
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2019年 / 42卷 / 05期
关键词：
d-Orthogonal polynomials; d-Dimensional vectors of linear forms; Recurrence relations; Linear combinations of d-orthogonal polynomials; Chebyshev d-orthogonal polynomials; Associated and co-recursive d-orthogonal polynomials; SEMICLASSICAL CHARACTER; INVERSE PROBLEM; SEQUENCES;
D O I：
10.1007/s40840-017-0589-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The regularity of a linear combination of r consecutive elements of a monic d-orthogonal polynomial sequence has been studied when (r-1) is a multiple of d. This problem can be solved without the introduction of the concept of d-quasi-orthogonality. In the present contribution, we deal with the problem of d-orthogonality of a linear combination of two elements of a monic d-orthogonal polynomial sequence. This problem is also equivalent to the study the regularity of the left product of a linear form by a matrix polynomial of degree one.
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页码：2009 / 2038
页数：30
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