Bad boundary behavior in star-invariant subspaces I

Andreas Hartmann; William T. Ross

doi:10.1007/s11512-012-0172-x

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Home > Journals > Ark. Mat. > Volume 52 > Issue 1 > Article

April 2014 Bad boundary behavior in star-invariant subspaces I

Andreas Hartmann, William T. Ross

Author Affiliations +

Andreas Hartmann,¹ William T. Ross²
¹Institut de Mathématiques de Bordeaux, Université de Bordeaux
²Department of Mathematics and Computer Science, University of Richmond

Ark. Mat. 52(1): 113-134 (April 2014). DOI: 10.1007/s11512-012-0172-x

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Abstract

We discuss the boundary behavior of functions in star-invariant subspaces (BH²)^⊥, where B is a Blaschke product. Extending some results of Ahern and Clark, we are particularly interested in the growth rates of functions at points of the spectrum of B where B does not admit a derivative in the sense of Carathéodory.

Funding Statement

The first author was supported by ANR FRAB: ANR-09-BLAN-0058-02. The authors would like to thank the referee for some useful comments and a simplification.

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Andreas Hartmann. William T. Ross. "Bad boundary behavior in star-invariant subspaces I." Ark. Mat. 52 (1) 113 - 134, April 2014. https://doi.org/10.1007/s11512-012-0172-x