Interpolation by multipliers on certain spaces of analytic functions.
Weighted composition operators on Bergman and Dirichlet spaces.
Operators acting on certain Banach spaces of analytic functions.
Spatial decay estimates for a class of nonlinear damped hyperbolic equations.
Operators on spaces of analytic functions
Let be the operator of multiplication by z on a Banach space of functions analytic on a plane domain G. We say that is polynomially bounded if for every polynomial p. We give necessary and sufficient conditions for to be polynomially bounded. We also characterize the finite-codimensional invariant subspaces and derive some spectral properties of the multiplication operator in case the underlying space is Hilbert.
Erratum to "Operators on spaces of analytic functions" (Studia Math, 108 (1994), 49-54)
Commutants of certain multiplication operators on Hilbert spaces of analytic functions
This paper characterizes the commutant of certain multiplication operators on Hilbert spaces of analytic functions. Let be the operator of multiplication by z on the underlying Hilbert space. We give sufficient conditions for an operator essentially commuting with A and commuting with for some n>1 to be the operator of multiplication by an analytic symbol. This extends a result of Shields and Wallen.
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