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Fractional Derivatives in Spaces of Generalized Functions

Stojanović, Mirjana (2011)

Fractional Calculus and Applied Analysis

MSC 2010: 26A33, 46Fxx, 58C05 Dedicated to 80-th birthday of Prof. Rudolf GorenfloWe generalize the two forms of the fractional derivatives (in Riemann-Liouville and Caputo sense) to spaces of generalized functions using appropriate techniques such as the multiplication of absolutely continuous function by the Heaviside function, and the analytical continuation. As an application, we give the two forms of the fractional derivatives of discontinuous functions in spaces of distributions.

From Banach to distributions and currents

Pierre Dolbeault (2009)

Banach Center Publications

From Silva tempered ultradistributions to ultradistributions of exponential type

Sousa Pinto, J. (1993)

Portugaliae mathematica

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...

Functional Equations and Tempered Ultradistributions

Dušanka Perišić (1994)

Publications de l'Institut Mathématique

Functional equations and tempered ultradistributions.

Perišić, Dušanka (1994)

Publications de l'Institut Mathématique. Nouvelle Série

Functions which are Fourier transforms of distributions

Raimond A. Struble (1981)

Colloquium Mathematicae

Functions with Time and Frequency Gaps.

Jens M. Melenk, Georg Zimmermann (1995)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

Funktionentheoretische Charakterisierung der Topologie in Distributionenräumen.

Peter Paul Konder (1971)

Mathematische Zeitschrift

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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