کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8898411 | 1631376 | 2018 | 18 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The algebras of difference operators associated to Krall-Charlier orthogonal polynomials
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: The algebras of difference operators associated to Krall-Charlier orthogonal polynomials The algebras of difference operators associated to Krall-Charlier orthogonal polynomials](/preview/png/8898411.png)
چکیده انگلیسی
Krall-Charlier polynomials (cna;F)n are orthogonal polynomials which are also eigenfunctions of a higher order difference operator. They are defined from a parameter a (associated to the Charlier polynomials) and a finite set F of positive integers. We study the algebra DaF formed by all difference operators with respect to which the family of Krall-Charlier polynomials (cna;F)n are eigenfunctions. Each operator DâDaF is characterized by the so called eigenvalue polynomial λD: λD is the polynomial satisfying D(cna;F)=λD(n)cna;F. We characterize the algebra of difference operators DaF by means of the algebra of polynomials DÌaF={λâC[x]:λ(x)=λD(x),DâDaF}. We associate to the family (cna;F)n a polynomial ΩFa
and prove that, except for degenerate cases, the algebra DÌaF is formed by all polynomials λ(x) such that ΩFa divides λ(x)âλ(xâ1). We prove that this is always the case for a segment F (i.e., the elements of F are consecutive positive integers), and conjecture that it is also the case when the Krall-Charlier polynomials (cna;F)n are orthogonal with respect to a positive measure.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Approximation Theory - Volume 234, October 2018, Pages 64-81
Journal: Journal of Approximation Theory - Volume 234, October 2018, Pages 64-81
نویسندگان
Antonio J. Durán,