scholarly journals Direct and inverse theorems on the approximation of almost periodic functions in Besicovitch-Stepanets spaces

2021 ◽  
Vol 13 (3) ◽  
pp. 687-700
Author(s):  
A.S. Serdyuk ◽  
A.L. Shidlich
Keyword(s):  
Almost Periodic Functions ◽  
Moduli Of Smoothness ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Best Approximations ◽  
Approximation Theorems ◽  
Inverse Approximation ◽  
Direct And Inverse Theorems ◽  
Inverse Theorems

Direct and inverse approximation theorems are proved in the Besicovitch-Stepanets spaces $B{\mathcal S}^{p}$ of almost periodic functions in terms of the best approximations of functions and their generalized moduli of smoothness.

scholarly journals Direct and inverse approximation theorems of functions in the Orlicz type spaces 𝓢M

2019 ◽  
Vol 69 (6) ◽  
pp. 1367-1380 ◽  
Author(s):  
Stanislav Chaichenko ◽  
Andrii Shidlich ◽  
Fahreddin Abdullayev
Keyword(s):  
Fractional Order ◽  
Moduli Of Smoothness ◽  
Best Approximations ◽  
Approximation Theorems ◽  
Inverse Approximation ◽  
Type Spaces

Abstract In the Orlicz type spaces 𝓢M, we prove direct and inverse approximation theorems in terms of the best approximations of functions and moduli of smoothness of fractional order. We also show the equivalence between moduli of smoothness and Peetre K-functionals in the spaces 𝓢M.

Almost periodic functions

Mathematika ◽  
1955 ◽  
Vol 2 (2) ◽  
pp. 128-131 ◽  
Author(s):  
J. D. Weston
Keyword(s):  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions

scholarly journals Almost periodic functions and hyperbolic counting

2018 ◽  
Vol 14 (09) ◽  
pp. 2343-2368
Author(s):  
Giacomo Cherubini
Keyword(s):  
Asymptotic Variance ◽  
Limiting Distribution ◽  
Almost Periodic Functions ◽  
Specific Class ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Circle Problem

We prove the existence of asymptotic moments and an estimate on the tails of the limiting distribution for a specific class of almost periodic functions. Then we introduce the hyperbolic circle problem, proving an estimate on the asymptotic variance of the remainder that improves a result of Chamizo. Applying the results of the first part we prove the existence of limiting distribution and asymptotic moments for three functions that are integrated versions of the remainder, and were considered originally (with due adaptations to our settings) by Wolfe, Phillips and Rudnick, and Hill and Parnovski.

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