Faltung hypersingulärer Integraloperatoren.
Finite symmetric trilinear integral transform of distributions. II.
Fourier inversion of distributions on projective spaces
We show that the Fourier-Laplace series of a distribution on the real, complex or quarternionic projective space is uniformly Cesàro-summable to zero on a neighbourhood of a point if and only if this point does not belong to the support of the distribution.
Fourier -transform of distributions
Fourier transform and distributional representation of the gamma function leading to some new identities.
Fourier transforms in generalized Fock spaces.
Fourier-Wigner transforms and Liouville's theorems for the sub-Laplacian on the Heisenberg group
The sub-Laplacian on the Heisenberg group is first decomposed into twisted Laplacians parametrized by Planck's constant. Using Fourier-Wigner transforms so parametrized, we prove that the twisted Laplacians are globally hypoelliptic in the setting of tempered distributions. This result on global hypoellipticity is then used to obtain Liouville's theorems for harmonic functions for the sub-Laplacian on the Heisenberg group.
From Silva tempered ultradistributions to ultradistributions of exponential type
Front d'onde analytique et décomposition microlocale des distributions
On étudie en détail une décomposition microlocale analytique de la distribution suivant des distributions singulières en un seul point et dans une seule codirection. Cette décomposition est obtenue à partir d’opérateurs Fourier-Intégraux à phases complexes.On utilise ensuite cet outil pour démontrer le théorème de décomposition du front d’onde analytique des distributions. On établit également des théorèmes concernant la représentation globale des distributions comme sommes de valeurs au bord...
Functions with Time and Frequency Gaps.
Fuzzy transforms in image compression and fusion
An overview of direct and inverse fuzzy transforms of three types is given and applications to data processing are considered. The construction and some important properties of fuzzy transforms are presented on the theoretical level. Three applications of -transform to data processing have been chosen: compressional and reconstruction of data, removing noise and data fusion. All of them successively exploit the filtering property of the inverse fuzzy transform.