Fourier Integrals Of Functions Research Articles

Almost everywhere convergence of Fourier integrals revisited

A condition of proved worth guarantees almost everywhere convergence of Fourier integrals of functions from an essentially wider class than known earlier.

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

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.