# Cyclic inner functions in growth classes and applications to approximation problems

@inproceedings{Malman2022CyclicIF, title={Cyclic inner functions in growth classes and applications to approximation problems}, author={Bartosz Malman}, year={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 for all z ∈ D , and ( ii ) sup n k θp n k ∞ < ∞ , are incompatible, i.e., cannot be satisﬁed simultaneously. In this note we discuss and apply a consequence of a result by Thomas Ransford from [13], which shows that if we relax the second condition to allow for arbitrarily slow growth of the sequence…

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