(last updated 2006-10-03)
Currently available preprint(s)
- Finite Rank Toeplitz Operators on the Bergman space
Proves that if a Toeplitz operator has a symbol which is a
finite complex measure, then it has finite rank if and
only if the measure is a finite sum of point masses.
- Interpolating sequences in the Bergman space and the d-bar
equation in weighted Lp
Shows that a sequence in the unit disk which is separated in the
hyperbolic metric is an interpolating sequence for the Bergman
space if and only if there exists a bounded solution operator
for the d-bar equation in a related weighted Lp space,
(0 < p < \infty)
- Generalized interpolating sequences for Bergman spaces
Describes a general method of interpolation, and shows that a
sequence in the unit disk is a general interpolating sequence if and
only if it satisfies K. Seip's uniform upper density criterion
(without any separation assumption). The result in
the previous preprint is also extended in the same way. The
result also encompasses M. Krosky and A. Schuster's
multiple interpolation criterion.
- Finite unions of interpolating sequences for Hardy
spaces.
Provides two new conditions on a sequence in the unit disk that
are equivalent to it being a finite union of interpolating
sequences for the Hardy spaces of the unit disk. Several such
conditions were treated in a unified way by P. Duren and
A. Schuster in a 2002 paper. This preprint also provides
a simpler proof of one of their equivalent conditions. We make
use of the concept of general interpolation introduced in
the previous preprint.
luecking @ comp . uark . edu