*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. (This has been published in the Proc. of the AMS, vol. 136 (2008), pages 1717-1723, with minor corrections.)- PDF file (159K).

*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)*Interpolation without separation in 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.- On the Math archives (272 K)

*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*interpolation schemes*introduced in the previous preprint.*Interpolation schemes in weighted Bergman spaces*

The methods of number 3 above are extended to Bergman spaces with weights more general than those considered there.

luecking @ comp . uark . edu