Geodesic
A note of some approximation theorems of functions on the Lguerre hypergroup
Filomat, Tome 37 (2023) no. 6, p. 1959

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DOI

This paper uses some basic notions and results on the Laguerre hypergroup K = [0, +∞) × R to study some problems in the theory of approximation of functions in the space L 2 α (K). Analogues of the direct Jackson theorems of approximations for the modulus of smoothness (of arbitrary order) constructed by using the generalized translation operators on K are proved. The Nikolskii-Stechkin inequality is also obtained. In conclusion of this work, we show that the modulus of smoothness and the K-functionals constructed from the Sobolev-type space corresponding to the Laguerre operator L α are equivalent.
DOI : 10.2298/FIL2306959T
Classification : 33D15, 33E30, 44A20
Keywords: Laguerre hypergroup, Fourier-Laguerre transform, Generalized translation operators, Direct Jackson theorems, K- functionals, Modulus of smoothness 
O Tyr; R Daher. A note of some approximation theorems of functions on the Lguerre hypergroup. Filomat, Tome 37 (2023) no. 6, p. 1959 . doi: 10.2298/FIL2306959T
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     title = {A note of some approximation theorems of functions on the {Lguerre} hypergroup},
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     doi = {10.2298/FIL2306959T},
     language = {en},
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