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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 functions...
This paper studies a two-variable zeta function attached to an algebraic
number field , introduced by van der Geer and Schoof, which is based on an analogue of
the Riemann-Roch theorem for number fields using Arakelov divisors. When this
function becomes the completed Dedekind zeta function of the field .
The function is a meromorphic function of two complex variables with polar divisor , and it satisfies the functional equation . We consider the
special case , where for this function...
We give a proof of an integral formula of Berndtsson which is related to the inversion of Fourier-Laplace transforms of -closed -forms in the complement of a compact convex set in .
On considère un polynôme , à coefficients réels non négatifs, à deux indéterminées. On montre que la connaissance des pôles des intégralesdonne des renseignements sur les racines du polynômes de Bernstein de . La détermination des pôles des intégrales peut se faire en utilisant certaines méthodes de Mellin. Des calculs explicites sont donnés.
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