Convergence of Fourier double series and Fourier integrals of functions on and after rotations of coordinates

Abstract

Let be a function vanishing for , where is sufficiently small, and with Fourier series (of the function considered in the square ) or Fourier integral (of the function considered in the plane ) convergent uniformly or almost everywhere over rectangles. It is shown that a rotation of the system of coordinates through can “damage” the convergence of the Fourier series or the Fourier integral of the resulting function.