Document Type
Article
Department
Mathematics (Pomona)
Publication Date
2005
Keywords
Riesz projection, Smirnov class, Herglotz integral, singular measure, Beurling's theorem, backward shift, pseudocontinuation
Abstract
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.
Rights Information
© 2005 American Mathematical Society
Terms of Use & License Information
Recommended Citation
Garcia, S.R., A *-closed subalgebra of the Smirnov class, Proc. Amer. Math. Soc. 133, no. 7, (2005), 2051–2059. MR2137871 (2005m:30040)
Comments
First published in Proceedings of the American Mathematical Society in Volume 133, Number 7, 2005, published by the American Mathematical Society.