Orthogonal Laurent polynomials of two real variables
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929505415725056 |
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| author | Cruz-Barroso, Ruymán Fernández, Lidia |
| author_facet | Cruz-Barroso, Ruymán Fernández, Lidia |
| contents | In this paper we consider an appropriate ordering of the Laurent monomials $x^{i}y^{j}$, $i,j \in \mathbb{Z}$ that allows us to study sequences of orthogonal Laurent polynomials of the real variables $x$ and $y$ with respect to a positive Borel measure $μ$ defined on $\mathbb{R}^2$ such that $\{ x=0 \}\cup \{ y=0 \} \not\in \textrm{supp}(μ)$. This ordering is suitable for considering the {\em multiplication plus inverse multiplication operator} on each varibale $\left( x+\frac{1}{x}\right.$ and $\left. y+\frac{1}{y}\right)$, and as a result we obtain five-term recurrence relations, Christoffel-Darboux and confluent formulas for the reproducing kernel and a related Favard's theorem. A connection with the one variable case is also presented, along with some applications for future research. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14303 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Orthogonal Laurent polynomials of two real variables Cruz-Barroso, Ruymán Fernández, Lidia Numerical Analysis 33C45, 42C05 In this paper we consider an appropriate ordering of the Laurent monomials $x^{i}y^{j}$, $i,j \in \mathbb{Z}$ that allows us to study sequences of orthogonal Laurent polynomials of the real variables $x$ and $y$ with respect to a positive Borel measure $μ$ defined on $\mathbb{R}^2$ such that $\{ x=0 \}\cup \{ y=0 \} \not\in \textrm{supp}(μ)$. This ordering is suitable for considering the {\em multiplication plus inverse multiplication operator} on each varibale $\left( x+\frac{1}{x}\right.$ and $\left. y+\frac{1}{y}\right)$, and as a result we obtain five-term recurrence relations, Christoffel-Darboux and confluent formulas for the reproducing kernel and a related Favard's theorem. A connection with the one variable case is also presented, along with some applications for future research. |
| title | Orthogonal Laurent polynomials of two real variables |
| topic | Numerical Analysis 33C45, 42C05 |
| url | https://arxiv.org/abs/2404.14303 |