A Riesz representation formula for super-biharmonic functions.
A factorization theorem for square area-integrable analytic functions.
Comparisions of ideal structures in algebras of analytic functions of several complex variables.
A comparison between the closed modular ideals in l...(w) and L...(w).
An Hadamard maximum principle for the biplacian on hyperbolic manifolds
We prove the existence of a maximum principle for operators of the type , for weights with subharmonic. It is associated with certain simply connected subdomains that are produced by a Hele-Shaw flow emanating from a given point in the domain. For constant weight, these are the circular disks in the domain. The principle is equivalent to the following statement. THEOREM. Suppose is logarithmically subharmonic on the unit disk, and that the weight times area measure is a reproducing measure...
An invariant subspace of the Bergman space having the codimension two property.
Invariant subspaces on multiply connected domains.
The lattice of invariant subspaces of several Banach spaces of analytic functions on the unit disk, for example the Bergman spaces and the Dirichlet spaces, have been studied recently. A natural question is to what extent these investigations carry over to analogously defined spaces on an annulus. We consider this question in the context of general Banach spaces of analytic functions on finitely connected domains Ω. The main result reads as follows: Assume that B is a Banach space of analytic functions...
Perron-Frobenius operators and the Klein-Gordon equation
For a smooth curve and a set in the plane , let be the space of finite Borel measures in the plane supported on , absolutely continuous with respect to the arc length and whose Fourier transform vanishes on . Following [12], we say that is a Heisenberg uniqueness pair if . In the context of a hyperbola , the study of Heisenberg uniqueness pairs is the same as looking for uniqueness sets of a collection of solutions to the Klein-Gordon equation. In this work, we mainly address the...
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