Goffman, C Waterman, D
Published in
Proceedings of the National Academy of Sciences of the United States of America

The localization theorems for Fourier series of functions of a single variable are classical and easy to prove. The situation is different for Fourier series of functions of several variables, even if one restricts consideration to rectangular, in particular square, partial sums. We show that the answer to the problem can be obtained by considering...

Rodin, V. A.
Published in
Mathematical Notes

In this paper we establish a general assertion relating the oscillation of the sequence of rectangular partial sums of a multiple Fourier series in a multiplicative system to the strong summability of this series. The systems of group generators are assumed to be uniformly bounded. Earlier these assertions were obtained by the author for the Walsh ...

Galstyan, S. Sh. Karagulyan, G. A.
Published in
Mathematical Notes

In this paper we establish the following results, which are the multidimensional generalizations of well-known theorems:Suppose that a functionf ∈C(Tm) has no intervals of constancy inTm; then there exists a homeomorphism ϕ:Tm →Tm such that the Fourier series of the superpositionF=f o ϕ is divergent with respect to rectangles almost everywhere; for...

Saakyan, A. A.
Published in
Mathematical Notes

The problem of Pringsheim uniform convergence of multiple Fourier series in the trigonometric system is considered. A multidimensional analog of Bohr's theorem on the uniform convergence of the Fourier series of a continuous function after a homeomorphic chance of variable is proved.

D'yachenko, M. I.
Published in
Mathematical Notes

In this paper, u-convergence problems for multiple Fourier series with monotone and with positive coefficients in the Lp metrics are considered.

D'yachenko, M. I.
Published in
Mathematical Notes

It follows from results of A. Yudin, V. Yudin, E. Belinskii, and I. Liflyand that if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$m \geqslant 2$$ \end{document} and...

Drozdov, S. M.
Published in
Fluid Dynamics

Steady quasiperiodic solutions of the Navier-Stokes equations in an infinite two-dimensional layer with quasiperiodic boundaries are obtained on the Reynolds number range 0

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

In this paper, we obtain the structural and geometric characteristics of some subsets of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathbb{T} $$\end{document}N =...

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...

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.