On the expansions of analytic functions on convex locally closed sets in exponential series.

Melikhov, S.N.; Momm, S.

Displaying similar documents to “On the expansions of analytic functions on convex locally closed sets in exponential series.”

On a space of smooth functions on a convex unbounded set in ℝn admitting holomorphic extension in ℂn

Il’dar Musin, Polina Yakovleva (2012)

Open Mathematics

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For some given logarithmically convex sequence M of positive numbers we construct a subspace of the space of rapidly decreasing infinitely differentiable functions on an unbounded closed convex set in ℝn. Due to the conditions on M each function of this space admits a holomorphic extension in ℂn. In the current article, the space of holomorphic extensions is considered and Paley-Wiener type theorems are established. To prove these theorems, some auxiliary results on extensions of holomorphic...

Asymptotics for the probability of connectedness and the distribution of number of components.

Bell, Jason P., Bender, Edward A., Cameron, Peter J., Richmond, L.Bruce (2000)

The Electronic Journal of Combinatorics [electronic only]

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When structures are almost surely connected.

Bell, Jason P. (2000)

The Electronic Journal of Combinatorics [electronic only]

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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.

On the convergence properties of basic series representing Clifford valued functions.

Abul-Ez, M. A., Constales, D. (2003)

International Journal of Mathematics and Mathematical Sciences

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The holomorphic extension of $C^{k}$ CR functions on tube submanifolds

Al Boggess (1998)

Annales Polonici Mathematici

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We show that a CR function of class $C^{k}$ , 0 ≤ k < ∞, on a tube submanifold of $ℂ^{n}$ holomorphically extends to the convex hull of the submanifold. The extension and all its derivatives through order k are shown to have nontangential pointwise boundary values on the original tube submanifold. The $C^{k}$ -norm of the extension is shown to be no bigger than the $C^{k}$ -norm of the original CR function.

Approximation in $ℂ^{N}$ .

Levenberg, Norm (2006)

Surveys in Approximation Theory (SAT)[electronic only]

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On the computation of Aden functions

Peter Maličký, Marianna Maličká (1991)

Applications of Mathematics

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The paper deals with the computation of Aden functions. It gives estimates of errors for the computation of Aden functions by downward reccurence.