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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Tangential limits of functions orthogonal to invariant subspaces


Author: David Protas
Journal: Trans. Amer. Math. Soc. 166 (1972), 163-172
MSC: Primary 30A72; Secondary 30A78
DOI: https://doi.org/10.1090/S0002-9947-1972-0293100-8
MathSciNet review: 0293100
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Abstract: For any inner function $\varphi$, let ${M^ \bot }$ be the orthogonal complement of $\varphi {H^2}$, in ${H^2}$, where ${H^2}$ is the usual Hardy space. The relationship between the tangential convergence of all functions in ${M^ \bot }$ and the finiteness of certain sums and integrals involving $\varphi$ is studied. In particular, it is shown that the tangential convergence of all functions in ${M^ \bot }$ is a stronger condition than the tangential convergence of $\varphi$, itself.


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Keywords: Blaschke product, inner function, Hardy space, tangential limit, invariant subspace, boundary behavior
Article copyright: © Copyright 1972 American Mathematical Society