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Generalized Cesàro Operators: Geometry of Spectra and Quasi-Nilpotency
For the class of Hardy spaces and standard weighted Bergman spaces of the unit disk we prove that the spectrum of a generalized Ces\`aro operator $T_g$ is unchanged if the symbol $g$ is perturbed to
Spectra of Generalized Cesàro Operators Acting on Growth Spaces
We study the spectrum of generalized Cesàro operators $$T_g$$Tg acting on the class of growth spaces $$A^{-\alpha }$$A-α. We show how the problem of determining the spectrum is related to boundedness
On model spaces and density of functions regular on the boundary
We characterize the model spaces KΘ in which functions with smooth boundary extensions are dense. It turns out that such approximation is possible if and only if the singular measure associated to
Constructions of some families of smooth Cauchy transforms
For a given Beurling-Carleson subset E of the unit circle T which has positive Lebesgue measure, we give explicit formulas for measurable functions supported on E such that their Cauchy transforms
On the problem of smooth approximations in de Branges-Rovnyak spaces and connections to subnormal operators
For the class of de Branges-Rovnyak spaces H(b) of the unit disk D defined by extreme points b of the unit ball of H, we study the problem of approximation of a general function in H(b) by a function
An abstract approach to approximations in spaces of pseudocontinuable functions
We give an abstract approach to approximations with a wide range of regularity classes X in spaces of pseudocontinuable functions K p θ, where θ is an inner function and p > 0. More precisely, we
Nearly invariant subspaces of de Branges spaces
We prove that the nearly invariant subspaces of a de Branges space which have no common zeros are precisely of the form an exponential function times a de Branges space.
Cyclic inner functions in growth classes and applications to approximation problems
It is well-known that for any inner function θ defined in the unit disk D the following two conditons: ( i ) there exists a sequence of polynomials { p n } n such that lim n →∞ θ ( z ) p n ( z ) = 1