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Entire elliptic Hankel convolution equations

M. Belhadj, J. J. Betancor (2003)

Bollettino dell'Unione Matematica Italiana

In this paper we characterize the entire elliptic Hankel convolutors on tempered distributions in terms of the growth of their Hankel transforms.

Fourier inversion of distributions on projective spaces

Francisco Javier González Vieli (2006)

Commentationes Mathematicae Universitatis Carolinae

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-Wigner transforms and Liouville's theorems for the sub-Laplacian on the Heisenberg group

Aparajita Dasgupta, M. W. Wong (2010)

Banach Center Publications

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.

Front d'onde analytique et décomposition microlocale des distributions

Pascal Laubin (1983)

Annales de l'institut Fourier

On étudie en détail une décomposition microlocale analytique de la distribution δ ( x - y ) 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...

Fuzzy transforms in image compression and fusion

Irina Perfilieva (2007)

Acta Mathematica Universitatis Ostraviensis

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 F -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.

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