Interpolation dans les algèbres de Hörmander

Abstract : We deal with interpolation problems in spaces ${\mathcal A}_p(\C)$ of entire functions such that $\sup_{z\in \C}\vert f(z)\vert e^{-Bp(z)}<\infty$, where $p$ is a weight function and $B$ is a certain positive constant. These spaces are algebras under the ordinary product of functions. They are called Hörmander algebras. The problem may be formulated as follows : given a discrete sequence of complex numbers $\{\alpha_j\}$ and a sequence of complex values $\{w_j\}$ satisfying $\sup_j\vert w_j\vert e^{-B'p(\alpha_j)}<\infty$ with a certain constant $B'>0$, under what conditions does there exist a function $f\in {\mathcal A}_p(\C)$ such that for all $j$,$f(\alpha_j)=w_j $?This problem was motivated by its applications to harmonic analysis and more precisely to convolution equations. We explore this field by applying certain of our results to mean-periodic functions. We are also concerned with these interpolation questions in several variables.
Document type :
Habilitation à diriger des recherches
Mathematics [math]. Université Louis Pasteur - Strasbourg I, 2008


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Submitted on : Monday, November 10, 2008 - 3:51:45 PM
Last modification on : Monday, November 10, 2008 - 4:26:47 PM

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Myriam Ounaïes. Interpolation dans les algèbres de Hörmander. Mathematics [math]. Université Louis Pasteur - Strasbourg I, 2008. <tel-00338027>

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