Geodesic
Estimates for Sobolev-orthonormal functions and generated by Laguerre functions
Problemy analiza, Tome 10 (2021) no. 1, pp. 23-37

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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 $\lambda_{r,n}^\alpha(x)$, $x\in[0, \infty)$.
Keywords: Sobolev-type inner product, Sobolev-orthonormal functions.
Mots-clés : Laguerre functions 
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     author = {R. M. Gadzhimirzaev},
     title = {Estimates for {Sobolev-orthonormal} functions and generated by {Laguerre} functions},
     journal = {Problemy analiza},
     pages = {23--37},
     publisher = {mathdoc},
     volume = {10},
     number = {1},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2021_10_1_a1/}
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R. M. Gadzhimirzaev. Estimates for Sobolev-orthonormal functions and generated by Laguerre functions. Problemy analiza, Tome 10 (2021) no. 1, pp. 23-37. http://geodesic.mathdoc.fr/item/PA_2021_10_1_a1/