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Semigroups associated to generalized polynomials and some classical formulas

✍ Scribed by Cristina Balderrama; Piotr Graczyk; Wilfredo Urbina

Publisher: Elsevier Science
Year: 2009
Tongue: English
Weight: 275 KB
Volume: 92
Category: Article
ISSN: 0021-7824
DOI: 10.1016/j.matpur.2009.05.006

No coin nor oath required. For personal study only.

✦ Synopsis

We study operator semigroups associated with a family of generalized orthogonal polynomials with Hermitian matrix entries. For this we consider a Markov generator sequence, and therefore a Markov semigroup, for the family of orthogonal polynomials on R related to the generalized polynomials. We give an expression of the infinitesimal generator of this semigroup and under the hypothesis of diffusion we prove that this semigroup is also Markov. We also give expressions for the kernel of this semigroup in terms of the one-dimensional kernels and obtain some classical formulas for the generalized orthogonal polynomials from the correspondent formulas for orthogonal polynomials on R.

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