Kuznetsov, D. F.
Published in
Computational Mathematics and Mathematical Physics

AbstractThis paper is devoted to the development and application of the Fourier method to the numerical solution of Ito stochastic differential equations. Fourier series are widely used in various fields of applied mathematics and physics. However, the method of Fourier series as applied to the numerical solution of stochastic differential equation...

Kuznetsov, D. F.
Published in
Computational Mathematics and Mathematical Physics

AbstractThis paper is devoted to the comparative analysis of the efficiency of using the Legendre polynomials and trigonometric functions for the numerical solution of Ito stochastic differential equations under the method of approximating multiple Ito and Stratonovich stochastic integrals based on generalized multiple Fourier series. Using the mul...

Ashurov, R. R.
Published in
Mathematical Notes

Abstract In this paper, we study the almost everywhere convergence of spherical partial sums of multiple Fourier series of functions from Sobolev classes. It is proved that almost everywhere convergence will take place under the same conditions on the order of smoothness of the expanded function as for multiple Fourier integrals; these conditions w...

Ydyrys, Aizhan Sarybekova, Lyazzat Tleukhanova, Nazerke
Published in
Open Engineering

We study the multipliers of multiple Fourier series for a regular system on anisotropic Lorentz spaces. In particular, the sufficient conditions for a sequence of complex numbers {λk}k∈Zn in order to make it a multiplier of multiple trigonometric Fourier series from Lp[0; 1]n to Lq[0; 1]n , p > q. These conditions include conditions Lizorkin theore...

D’yachenko, M. I. Nursultanov, E. D. Nursultanov, M. E.
Published in
Mathematical Notes

It was proved earlier that, for multiple Fourier series whose coefficients are monotone in each index, the classicalHardy–Littlewood theorem is not valid for p ≤ 2m/(m+1), where m is the dimension of the space. We establish how the theorem must be modified in this case.

Vyas, R. G. Darji, K. N.
Published in
Mathematical Notes

We obtain sufficient conditions for β-absolute convergence (0

Bloshanskaya, S. K. Bloshanskii, I. L. Lifantseva, O. V.
Published in
Mathematical Notes

Golubov, B. I.
Published in
Mathematical Notes

We introduce the notion of spherical jump of a function of several variables at a given point with respect to a homogeneous harmonic polynomial. Here, if the function is integrable over spheres of sufficiently small radius centered at the given point and is continuous at this point, then its spherical jump at this point with respect to any homogene...

Bakhvalov, A. N.
Published in
Mathematical Notes

We construct new examples of functions of bounded Λ-variation not continuous in Λ-variation. Using these examples, we show that, in the problem of the summability of multiple Fourier series by the Cesàro method of negative order, the condition of continuity in Λ-variation, is essential in contrast to the one-dimensional case.

Drozdov, S. M.
Published in
Fluid Dynamics

A steady flow induced by quasiperiodic temperature distributions at the boundaries is considered with reference to the example of fluid convection in a plane horizontal layer heated from below. A spectral-finite-difference method is employed to obtain convective vortex structures varying quasiperiodically along the horizontal coordinate. The proper...