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An Hadamard maximum principle for the biplacian on hyperbolic manifolds

Håkan Hedenmalm — 1999

Journées équations aux dérivées partielles

We prove the existence of a maximum principle for operators of the type Δ ω - 1 Δ , for weights ω with log ω 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 ω is logarithmically subharmonic on the unit disk, and that the weight times area measure is a reproducing measure...

Invariant subspaces on multiply connected domains.

Ali AbkarHakan Hedenmalm — 1998

Publicacions Matemàtiques

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

Francisco Canto-MartínHåkan HedenmalmAlfonso Montes-Rodríguez — 2014

Journal of the European Mathematical Society

For a smooth curve Γ and a set Λ in the plane 2 , let A C ( Γ ; Λ ) be the space of finite Borel measures in the plane supported on Γ , absolutely continuous with respect to the arc length and whose Fourier transform vanishes on Λ . Following [12], we say that ( Γ , Λ ) is a Heisenberg uniqueness pair if A C ( Γ ; Λ ) = { 0 } . In the context of a hyperbola Γ , the study of Heisenberg uniqueness pairs is the same as looking for uniqueness sets Λ of a collection of solutions to the Klein-Gordon equation. In this work, we mainly address the...

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