One Inequality of the Landau–Kolmogorov Type for Periodic Functions of Two Variables

2019 ◽  
Vol 71 (2) ◽  
pp. 179-189
Author(s):  
V. F. Babenko
Keyword(s):  
Periodic Functions ◽  
Kolmogorov Type ◽  
Functions Of Two Variables

scholarly journals On approximation, in the strong sense, of functions of two variables by trigonometric polynomials

2021 ◽  
pp. 20
Author(s):  
V.V. Lipovik ◽  
N.P. Khoroshko
Keyword(s):  
Strong Sense ◽  
Trigonometric Polynomials ◽  
Asymptotic Estimates ◽  
Periodic Functions ◽  
Functions Of Two Variables

In the paper, we have found order asymptotic estimates of approximations, in the strong sense, relative to given matrix of classes of continuous periodic functions of two variables by some trigonometric polynomials.

scholarly journals CASIMIR FORCE BETWEEN TWO PARALLEL PLATES WITH SMALL DISTORTIONS OF DIFFERENT TYPES

1994 ◽  
Vol 09 (27) ◽  
pp. 2515-2526 ◽  
Author(s):  
M. BORDAG ◽  
G.L. KLIMCHITSKAYA ◽  
V.M. MOSTEPANENKO
Keyword(s):  
Casimir Force ◽  
Fourier Coefficients ◽  
Perturbation Expansion ◽  
Perturbative Expansion ◽  
Distortion Function ◽  
Parallel Plates ◽  
Force Measurements ◽  
Periodic Functions ◽  
Functions Of Two Variables ◽  
Different Types

We investigate the corrections to the Casimir force between two parallel plates covered with distortions described by periodic functions of two variables. The periods of the distortions in both coordinates are suggested to be much smaller than the sizes of the plates. A general expression is obtained for the Casimir force in the form of a perturbation expansion with respect to the amplitude of the distortions divided by the distance between the plates. The coefficients of this expansion are expressed in terms of the Fourier coefficients of the distortion function up to fourth order. It is shown that the perturbative expansion starts from the second order and does not depend on the period of the distortions. Some characteristic examples are calculated for both longitudinal and hillock-type distortions. It is shown that the contribution of the distortions to the Casimir force may achieve some 10%. So it must be taken into account in precision Casimir force measurements.

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