Tuesday Seminar of Analysis

Date, time & place	Tuesday 16:00 - 17:30 156Room #156 (Graduate School of Math. Sci. Bldg.)
Organizer(s)	ISHIGE Kazuhiro, SAKAI Hidetaka, ITO Kenichi

16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Myriam Ounaies (Strasbourg大学数学科)
Intrepolation problems in H￥"ormander algebras

[ Abstract ]
We call Hörmander algebras the spaces

$A_p(\\mathbb C)$ of entire functions

$f$ such that, for all

$z$ in

$\\mathbb C$ , \\[|f(z)|\\le Ae^{Bp(z)},\\] where

$A$ and

$B$ are some positive constants (depending on

$f$ ) and

$p$ is a subharmonic weight. We consider the following interpolation problem : Given a discrete sequence

$\\{a_j\\}$ of complex numbers and a sequence of complex values

$\\{b_j\\}$ , under what conditions does there exist a function

$f\\in A_p(\\mathbb C)$ such that

$f(a_j)=b_j$ for all

$j$ ? In other words, what is the trace of

$A_p(\\mathbb C)$ on

$\\{a_j\\}$ ?
We say that

$\\{a_j\\}$ is an interpolating sequence if the trace is defined by the space of all

$\\{b_j\\}$ satisfying

$|b_j|\\le A'e^{B'p(a_j)}$ , for some constants

$A',B'>0$ .
We use Hörmander's

$L^2$ -estimates for the

$\\bar\\partial$ -equation to describe the trace when the weight

$p$ is radial and doubling and to characterize the interpolating sequences for more general weights.

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