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Intégrales trigonométriques et pseudofonctions

Francisco Javier González Vieli (1994)

Annales de l'institut Fourier

On étudie un analogue à plusieurs variables réelles de la théorie de Riemann des séries trigonométriques vue sous l’angle des pseudofonctions, en utilisant le laplacien intégral et la fonction de Riemann qui découle de ce choix.

Interpolating sequences, Carleson measures and Wirtinger inequality

Eric Amar (2008)

Annales Polonici Mathematici

Let S be a sequence of points in the unit ball of ℂⁿ which is separated for the hyperbolic distance and contained in the zero set of a Nevanlinna function. We prove that the associated measure μ S : = a S ( 1 - | a | ² ) δ a is bounded, by use of the Wirtinger inequality. Conversely, if X is an analytic subset of such that any δ -separated sequence S has its associated measure μ S bounded by C/δⁿ, then X is the zero set of a function in the Nevanlinna class of . As an easy consequence, we prove that if S is a dual bounded sequence...

Interpolation problems in cones. Nota I

Carlos A. Berenstein, Daniele Struppa (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In questa nota, si studiano problemi di interpolazione per varietà discrete in spazi di funzioni olomorfe in coni. In particolare si mostra come sia possibile estendere il Principio Fondamentale di Ehrenpreis ad equazioni di convoluzione nella spazio H c ( Ω ) , introdotto in [4] in connessione con problemi di fisica quantistica.

Interpolation problems in cones. Nota II

Carlos A. Berenstein, Daniele Struppa (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si estendono qui i risultati della nota precedente al caso di varietà non discrete. Ciò viene utilizzato per ottenere un teorema di rappresentazione per soluzioni di sistemi di equazioni di convoluzione in spazi di funzioni olomorfe in coni.

Intrinsic characterizations of distribution spaces on domains

V. Rychkov (1998)

Studia Mathematica

We give characterizations of Besov and Triebel-Lizorkin spaces B p q s ( ) and F p q s ( ) in smooth domains n via convolutions with compactly supported smooth kernels satisfying some moment conditions. The results for s ∈ ℝ, 0 < p,q ≤ ∞ are stated in terms of the mixed norm of a certain maximal function of a distribution. For s ∈ ℝ, 1 ≤ p ≤ ∞, 0 < q ≤ ∞ characterizations without use of maximal functions are also obtained.

Inverse Fourier transform

Leonede De Michele, Marina Di Natale, Delfina Roux (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this paper a very general method is given in order to reconstruct a periodic function f knowing only an approximation of its Fourier coefficients.

Inversion Formulas for the q-Riemann-Liouville and q-Weyl Transforms Using Wavelets

Fitouhi, Ahmed, Bettaibi, Néji, Binous, Wafa (2007)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 42A38, 42C40, 33D15, 33D60This paper aims to study the q-wavelets and the continuous q-wavelet transforms, associated with the q-Bessel operator for a fixed q ∈]0, 1[. Using the q-Riemann-Liouville and the q-Weyl transforms, we give some relations between the continuous q-wavelet transform, studied in [3], and the continuous q-wavelet transform associated with the q-Bessel operator, and we deduce formulas which give the inverse operators of the q-Riemann-Liouville and...

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