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Displaying 1 – 18 of 18

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

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...

On a two-variable zeta function for number fields

Jeffrey C. Lagarias, Eric Rains (2003)

Annales de l’institut Fourier

This paper studies a two-variable zeta function $Z_{K} (w, s)$ attached to an algebraic number field $K$ , 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 $w = 1$ this function becomes the completed Dedekind zeta function ${\hat{ζ}}_{K} (s)$ of the field $K$ . The function is a meromorphic function of two complex variables with polar divisor $s (w - s)$ , and it satisfies the functional equation $Z_{K} (w, s) = Z_{K} (w, w - s)$ . We consider the special case $K = ℚ$ , where for $w = 1$ this function...

On an integral formula of Berndtsson related to the inversion of the Fourier-Laplace transform of $\bar{\partial}$ -closed $(n, n - 1)$ -forms

Telemachos Hatziafratis (2004)

Annales mathématiques Blaise Pascal

We give a proof of an integral formula of Berndtsson which is related to the inversion of Fourier-Laplace transforms of $\bar{\partial}$ -closed $(n, n - 1)$ -forms in the complement of a compact convex set in $ℂ^{n}$ .

On the indicator of growth of entire functions of exponential type in infinite dimensional spaces and the Levi problem in infinite dimensional projective spaces.

Nishihara, Masaru (1995)

Portugaliae Mathematica

Optimal error of analytic continuation from a finite set with inaccurate data in Hilbert spaces of holomorphic functions.

Maergojz, L.S., Fedotov, A.M. (2001)

Sibirskij Matematicheskij Zhurnal

Ordre d'une fonction de Dirichlet entière de plusieurs variables complexes

Daoud, S. (1985/1986)

Portugaliae mathematica

Currently displaying 1 – 18 of 18

Page 1

Displaying 1 – 18 of 18

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

On a two-variable zeta function for number fields

On an integral formula of Berndtsson related to the inversion of the Fourier-Laplace transform of $\bar{\partial}$ -closed $(n, n - 1)$ -forms

On $(p, q)$ -th order of a function of two complex variables analytic in the unit polydisc

On the class of entire Dirichlet functions of several complex variables having finite order point

On the Fourier-Laplace representation of analytic functions in tube domains.

On the geometric means of an entire function of several complex variables represented by multiple Dirichlet series.

On the growth of entire functions of n complex variables

On the growth of proper polynomial mappings

On the indicator of growth of entire functions of exponential type in infinite dimensional spaces and the Levi problem in infinite dimensional projective spaces.

On the mean values of an entire function represented by Dirichlet series of several complex variables.

On the shared values of entire functions and their partial differential polynomials in Cn*.

On the space of integral Dirichlet functions of several complex variables

On uniform convergence for (mu,nu)-type rational approximants in $C^{n} \cdot$ II.

On values of homogeneous polynomials in discrete sets of points

Opérateurs différentiels d'ordre infini dans des espaces de fonctions entières

Optimal error of analytic continuation from a finite set with inaccurate data in Hilbert spaces of holomorphic functions.

Ordre d'une fonction de Dirichlet entière de plusieurs variables complexes

Currently displaying 1 – 18 of 18