(last updated 2023-04-03)

Currently available preprint(s)

  1. 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.)
  2. 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)
  3. 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.
  4. 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.
  5. 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