Estimates for Sobolev-orthonormal functions and generated by Laguerre functions

R. M. Gadzhimirzaev

Problemy analiza, Tome 10 (2021) no. 1, pp. 23-37.

Résumé

In this paper, we consider the system of functions $\lambda_{r,n}^\alpha(x)$ $(n=0, 1,\ldots)$, $\alpha>-1$, $r\in\mathbb{N}$, orthonormal with respect to a Sobolev-type inner product and generated by the system of Laguerre functions. Using asymptotic formulas for the Laguerre polynomials, we obtain estimates for functions $\lambda_{r,n}^\alpha(x)$, $x\in[0, \infty)$.

Détail

Keywords: Sobolev-type inner product, Sobolev-orthonormal functions.
Mots-clés : Laguerre functions

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