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A  -closed subalgebra of the Smirnov class |
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| Authors: | Stephan Ramon Garcia |
| Institution: | Department of Mathematics, University of California at Santa Barbara, Santa Barbara, California 93106-3080 |
| Abstract: | We study real Smirnov functions and investigate a certain  -closed subalgebra of the Smirnov class  containing them. Motivated by a result of Aleksandrov, we provide an explicit representation for the space  . This leads to a natural analog of the Riesz projection on a certain quotient space of  for  . We also study a Herglotz-like integral transform for singular measures on the unit circle  . |
| Keywords: | Riesz projection Smirnov class Herglotz integral singular measure Beurling's theorem backward shift pseudocontinuation |
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