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Mathematics (Pomona)

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Riesz projection, Smirnov class, Herglotz integral, singular measure, Beurling's theorem, backward shift, pseudocontinuation


We study real Smirnov functions and investigate a certain *-closed subalgebra of the Smirnov class N^+ containing them. Motivated by a result of Aleksandrov, we provide an explicit representation for the space H^p ∩ H^p [overscore over the second H^p]. This leads to a natural analog of the Riesz projection on a certain quotient space of L^p for p ϵ (0, 1). We also study a Herglotz-like integral transform for singular measures on the unit circle ∂D.


First published in Proceedings of the American Mathematical Society in Volume 133, Number 7, 2005, published by the American Mathematical Society.

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© 2005 American Mathematical Society

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