On the subspaces of analytic and antianalytic functions

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dc.contributor.author Fedorov, Sergei en
dc.date.accessioned 2009-08-28T03:21:22Z en
dc.date.available 2009-08-28T03:21:22Z en
dc.date.issued 1998-09 en
dc.identifier.citation Department of Mathematics - Research Reports-404 (1998) en
dc.identifier.issn 1173-0889 en
dc.identifier.uri http://hdl.handle.net/2292/5027 en
dc.description.abstract The problem of description of those positive weights on the boundary $Gamma$ of a finitely connected domain $Omega$ for which the angle in a weighted $L_2$ space on $Gamma$ between the linear space ${cal R}(Omega)$ of all rational functions on $bar{bf {C}}$ with poles outside of $Clos Omega$ and the linear space ${cal R}(Omega)_-={bar{f}vert fin {cal R}(Omega)}$ of antianalytic rational functions, is a natural analog of the problem solved in a famous Helson-Szeg"o theorem. In this paper we solve more general problem and give a complete description (in terms of necessary and sufficient conditions) of those positive weights $w$ on $Gamma$ for which the sum of the closures in $L_2(Gamma, w)$ of the subspaces ${cal R}(Omega)$ and ${cal R}(Omega)_-$ is closed and their intersection is finite dimensional. The given description is similar to that one in the Helson-Sarason Theorem, i.e. the "modified" weight should satisfy the Muckenhoupt condition. en
dc.publisher Department of Mathematics, The University of Auckland, New Zealand en
dc.relation.ispartofseries Research Reports - Department of Mathematics en
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm en
dc.source.uri http://www.math.auckland.ac.nz/Research/Reports/view.php?id=404 en
dc.title On the subspaces of analytic and antianalytic functions en
dc.type Technical Report en
dc.subject.marsden Fields of Research::230000 Mathematical Sciences::230100 Mathematics en
dc.rights.holder The author(s) en

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