# An abstract approach to approximations in spaces of pseudocontinuable functions

@inproceedings{Limani2021AnAA, title={An abstract approach to approximations in spaces of pseudocontinuable functions}, author={Adem Limani and Bartosz Malman}, year={2021} }

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 demonstrate a general principle, attributed to A. B. Aleksandrov, which asserts that if a certain linear manifold X is dense in the space of pseudocontinuable functions K p0 θ , for some p0 > 0, then X is in fact dense in K p θ, for all p > 0. Moreover, for a rich class of Banach spaces of analytic…

## 3 Citations

Remarks on cyclic inner functions in growth classes and applications to approximation problems

- Mathematics
- 2022

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…

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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 model spaces and density of functions smooth on the boundary

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We characterize the model spaces KΘ in which functions with smooth boundary extensions are dense. It is shown that such approximations are possible if and only if the singular measure associated to…

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