From: BrendaSueCook (brenda@math.missouri.edu)
Date: Thu Apr 26 2007 - 09:18:30 CDT
Harmonic Analysis Seminar
Friday, April 27, 2007
4-4:50 PM
MATH 312
Wilfredo Urbina, Universidad Central de Venezuela (UCV)
Fractional Integration and Fractional Differentiation for
$d$-dimensional Jacobi Expansions" (joint work with Cristina
Balderrama, UCV)
Abstract: In this work we consider an alternative orthogonal
decomposition of the space $L2$ associated to the $d$-dimensional
Jacobi measure in order to obtain an analogous result to P.A. Meyer's
Multipliers Theorem for $d$-dimensional Jacobi expansions. Then we
define and study the Fractional Integral, the Fractional Derivative and
the Bessel potentials induced by the Jacobi operator. We also obtain a
characterization of the Sobolev or potential spaces and a version of
Calder\'on's reproduction formula for the $d$-dimensional Jacobi
measure.
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