Jackson's inequality for mean-square approximations of periodic functions by trigonometric polynomials on a uniform grid

1988 ◽  
Vol 43 (4) ◽  
pp. 264-272
Author(s):  
A. G. Babenko
Keyword(s):  
Trigonometric Polynomials ◽  
Uniform Grid ◽  
Mean Square ◽  
Periodic Functions ◽  
Jackson’S Inequality ◽  
Jackson's Inequality

Precise constant in Jackson's inequality for continuous periodic functions

1982 ◽  
Vol 32 (5) ◽  
pp. 818-821 ◽  
Author(s):  
N. P. Korneichuk
Keyword(s):  
Periodic Functions ◽  
Jackson’S Inequality ◽  
Precise Constant ◽  
Jackson's Inequality

Sharpness of Jackson's inequality for individual functions

1990 ◽  
Vol 42 (11) ◽  
pp. 1311-1316 ◽  
Author(s):  
O. V. Davydov
Keyword(s):  
Jackson’S Inequality ◽  
Jackson's Inequality

24.—Mean-square Convergence of Non-harmonic Trigonometrical Series

1976 ◽  
Vol 75 (4) ◽  
pp. 297-323
Author(s):  
J. Cossar
Keyword(s):  
Fourier Series ◽  
Periodic Function ◽  
Mean Square ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Real Numbers ◽  
Trigonometrical Series ◽  
Fixed Positive Number ◽  
Mean Square Convergence ◽  
The Difference

SynopsisThe series considered are of the form , where Σ | cn |2 is convergent and the real numbers λn (the exponents) are distinct. It is known that if the exponents are integers, the series is the Fourier series of a periodic function of locally integrable square (the Riesz-Fischer theorem); and more generally that if the exponents are not necessarily integers but are such that the difference between any pair exceeds a fixed positive number, the series is the Fourier series of a function of the Stepanov class, S2, of almost periodic functions.We consider in this paper cases where the exponents are subject to less stringent conditions (depending on the coefficients cn). Some of the theorems included here are known but had been proved by other methods. A fuller account of the contents of the paper is given in Sections 1-5.

scholarly journals Approximation of multivariate periodic functions by trigonometric polynomials based on rank-1 lattice sampling

2015 ◽  
Vol 31 (4) ◽  
pp. 543-576 ◽  
Author(s):  
Lutz Kämmerer ◽  
Daniel Potts ◽  
Toni Volkmer
Keyword(s):  
Trigonometric Polynomials ◽  
Periodic Functions
Sign in / Sign up

Export Citation Format

Share Document