Geodesic
Bessel harmonic analysis and approximation of functions on the half-line
Izvestiya. Mathematics , Tome 71 (2007) no. 5, pp. 1001-1048

Voir la notice de l'article provenant de la source Math-Net.Ru

We study problems of approximation of functions on $[0, +\infty)$ in the metric of $L_p$ with power weight using generalized Bessel shifts. We prove analogues of direct Jackson theorems for the modulus of smoothness of arbitrary order defined in terms of generalized Bessel shifts. We establish the equivalence of the modulus of smoothness and the $K$-functional. We define function spaces of Nikol'skii–Besov type and describe them in terms of best approximations. As a tool for approximation, we use a certain class of entire functions of exponential type. In this class, we prove analogues of Bernstein's inequality and others for the Bessel differential operator and its fractional powers. The main tool we use to solve these problems is Bessel harmonic analysis. 
@article{IM2_2007_71_5_a4,
     author = {S. S. Platonov},
     title = {Bessel harmonic analysis and approximation of functions on the half-line},
     journal = {Izvestiya. Mathematics },
     pages = {1001--1048},
     publisher = {mathdoc},
     volume = {71},
     number = {5},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2007_71_5_a4/}
}
TY  - JOUR
AU  - S. S. Platonov
TI  - Bessel harmonic analysis and approximation of functions on the half-line
JO  - Izvestiya. Mathematics 
PY  - 2007
SP  - 1001
EP  - 1048
VL  - 71
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2007_71_5_a4/
LA  - en
ID  - IM2_2007_71_5_a4
ER  - 
%0 Journal Article
%A S. S. Platonov
%T Bessel harmonic analysis and approximation of functions on the half-line
%J Izvestiya. Mathematics 
%D 2007
%P 1001-1048
%V 71
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2007_71_5_a4/
%G en
%F IM2_2007_71_5_a4
S. S. Platonov. Bessel harmonic analysis and approximation of functions on the half-line. Izvestiya. Mathematics , Tome 71 (2007) no. 5, pp. 1001-1048. http://geodesic.mathdoc.fr/item/IM2_2007_71_5_a4/