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Transactions of the American Mathematical Society
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
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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DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0293100-8
PII: S 0002-9947(1972)0293100-8
Keywords: Blaschke product, inner function, Hardy space, tangential limit, invariant subspace, boundary behavior
Article copyright: © Copyright 1972 American Mathematical Society