| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] UNESP Univ Estadual Paulista, Dept Matemat Aplicada, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil
[2] Univ Fed Maranhao, Dept Matemat, BR-65080805 Sao Luis, MA - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | ACTA APPLICANDAE MATHEMATICAE; v. 164, n. 1, p. 137-154, DEC 2019. |
| Web of Science Citations: | 0 |
| Abstract | |
When a measure psi(x), then the coefficients of the recurrence relation of the orthogonal polynomials in x are known to satisfy the so-called Toda lattice formulas as functions of t. In this paper we consider a modification of the form e-t(px+q/x) of measures or, more generally, of moment functionals, associated with orthogonal L-polynomials and show that the coefficients of the recurrence relation of these L-orthogonal polynomials satisfy what we call an extended relativistic Toda lattice. Most importantly, we also establish the so called Lax pair representation associated with this extended relativistic Toda lattice. These results also cover the (ordinary) relativistic Toda lattice formulations considered in the literature by assuming either p=0. However, as far as Lax pair representation is concern, no complete Lax pair representations were established before for the respective relativistic Toda lattice formulations. Some explicit examples of extended relativistic Toda lattice and Langmuir lattice are also presented. As further results, the lattice formulas that follow from the three term recurrence relations associated with kernel polynomials on the unit circle are also established. (AU) | |
| FAPESP's process: | 17/12324-6 - Orthogonal polynomials on the unit circle and related studies |
| Grantee: | Alagacone Sri Ranga |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 16/09906-0 - Harmonic analysis, approximation theory and applications |
| Grantee: | Dimitar Kolev Dimitrov |
| Support Opportunities: | Research Projects - Thematic Grants |