Extension sets for real analytic functions and applications to Radon transforms.

Arguedas, Vernor; Estrada, Ricardo

Displaying similar documents to “Extension sets for real analytic functions and applications to Radon transforms.”

Extension of separately analytic functions and applications to range characterization of the exponential Radon transform

Ozan Öktem (1998)

Annales Polonici Mathematici

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We consider the problem of characterizing the range of the exponential Radon transform. The proof uses extension properties of separately analytic functions, and we prove a new theorem about extending such functions.

On entire functions which transform straight lines into parabolas

Hiroshi Haruki (1975)

Colloquium Mathematicae

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A support theorem for the complex Radon transform.

A. B. Sekerin (1999)

Collectanea Mathematica

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The support theorem for the complex Radon transform of distributions.

A. B. Sekerin (2004)

Collectanea Mathematica

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Asymptotic properties of the Radon transform in $ℝ^{n}$ .

Bray, William O. (1986)

Publications de l'Institut Mathématique. Nouvelle Série

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Integro-differential-difference equations associated with the Dunkl operator and entire functions

Néjib Ben Salem, Samir Kallel (2004)

Commentationes Mathematicae Universitatis Carolinae

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In this work we consider the Dunkl operator on the complex plane, defined by $𝒟_{k} f (z) = \frac{d}{d z} f (z) + k \frac{f (z) - f (- z)}{z}, k \geq 0 .$ We define a convolution product associated with $𝒟_{k}$ denoted $*_{k}$ and we study the integro-differential-difference equations of the type $μ *_{k} f = \sum_{n = 0}^{\infty} a_{n, k} 𝒟_{k}^{n} f$ , where $(a_{n, k})$ is a sequence of complex numbers and $μ$ is a measure over the real line. We show that many of these equations provide representations for particular classes of entire functions of exponential type.

Polya's theorem for non-entire functions

Yoshino, Kunio

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Tauberian theorems for vector-valued Fourier and Laplace transforms

Ralph Chill (1998)

Studia Mathematica

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Let X be a Banach space and $f \in L_{l}^{1} o c (ℝ; X)$ be absolutely regular (i.e. integrable when divided by some polynomial). If the distributional Fourier transform of f is locally integrable then f converges to 0 at infinity in some sense to be made precise. From this result we deduce some Tauberian theorems for Fourier and Laplace transforms, which can be improved if the underlying Banach space has the analytic Radon-Nikodym property.