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Invariant subspaces on multiply connected domains
Abkar, A. (Lund University (Suècia). Department of Mathematics)
Hedenmalm, H. (Lund University (Suècia). Department of Mathematics)

Data: 1998
Resum: The lattice of invariant subspaces of several Banach spaces of analytic functions on the unit disk, for example the Bergman spaces and the Dirichlet spaces, have been studied recently. A natural question is to what extent these investigations carry over to analogously defined spaces on an annulus. We consider this question in the context of general Banach spaces of analytic functions on finitely connected domains Ω. The main result reads as follows: Assume that B is a Banach space of analytic functions satisfying some conditions on the domain Ω. Assume further that M(B) is the set of all multipliers of B. Let Ω1 be a domain obtained from Ω by adding some of the bounded connectivity components of C\Ω. Also, let B1 be the closed subspace of B of all functions that extend analytically to Ω1. Then the mapping I 7→ clos(I · M(B)) gives a one-to-one correspondence between a class of multiplier invariant subspaces I of B1, and a class of multiplier invariant subspaces J of B. The inverse mapping is given by J 7→ J ∩ B1.
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: Article ; recerca ; article ; publishedVersion
Publicat a: Publicacions Matemàtiques, V. 42 n. 2 (1998) p. 521-557, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_42298_15

37 p, 248.2 KB

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