An inverse theorem of approximation theory of periodic functions in various metrics

1992 ◽  
Vol 52 (2) ◽  
pp. 791-798
Author(s):  
N. A. Il'yasov
Keyword(s):  
Approximation Theory ◽  
Inverse Theorem ◽  
Periodic Functions

On approximation in Weighted Orlicz spaces

2012 ◽  
Vol 62 (1) ◽  
Author(s):  
Ali Guven ◽  
Daniyal Israfilov
Keyword(s):  
Approximation Theory ◽  
Orlicz Spaces ◽  
Trigonometric Approximation ◽  
Inverse Theorem ◽  
Lipschitz Classes

AbstractAn inverse theorem of the trigonometric approximation theory in Weighted Orlicz spaces is proved and the constructive characterization of the generalized Lipschitz classes defined in these spaces is obtained.

scholarly journals On extremal problems of approximation theory for classes of functions of two discrete variables in $l^2_{q,p}$

2021 ◽  
Vol 15 ◽  
pp. 60
Author(s):  
S.B. Vakarchuk ◽  
M.B. Vakarchuk
Keyword(s):  
Approximation Theory ◽  
Extremal Problems ◽  
Discrete Variables ◽  
Periodic Functions

For classes of $2\pi$-periodic functions of two discrete variables, defined on grid set $\sigma_{q,p}$, we found exact values of Kolmogorov and linear quasiwidths of classes $W^{r,p}(l^2_{q,p})$ in $l^2_{q,p}$ space.

scholarly journals Smoothness and Function Spaces Generated by Homogeneous Multipliers

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Konstantin Runovski ◽  
Hans-Jürgen Schmeisser
Keyword(s):  
Fourier Transform ◽  
Approximation Theory ◽  
Differential Operators ◽  
Function Spaces ◽  
Explicit Representation ◽  
Periodic Functions ◽  
Homogeneous Functions ◽  
Representation Formulas ◽  
The Fourier Transform ◽  
And Function

Differential operators generated by homogeneous functionsψof an arbitrary real orders>0(ψ-derivatives) and related spaces ofs-smooth periodic functions ofdvariables are introduced and systematically studied. The obtained scale is compared with the scales of Besov and Triebel-Lizorkin spaces. Explicit representation formulas forψ-derivatives are obtained in terms of the Fourier transform of their generators. Some applications to approximation theory are discussed.

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