Pointwise and directional regularity of nonharmonic Fourier series

Stéphane Jaffard (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We investigate how the regularity of nonharmonic Fourier series is related to the spacing of their frequencies. This is obtained by using a transform which simultane- ously captures the advantages of the Gabor and Wavelet transforms. Applications to the everywhere irregularity of solutions of some PDEs are given. We extend these results to the anisotropic setting in order to derive directional irregularity criteria.

Domaines: Analyse classique [math.CA]

Stéphane Jaffard. Pointwise and directional regularity of nonharmonic Fourier series. Applied and Computational Harmonic Analysis, 2010, 22 (3), pp.251-266. ⟨hal-00798367⟩