On a Projection from One Co - Invariant Subspace onto Another in Character - Automorphic Hardy Space on a Multiply Connected Domain

2000 ◽  
Vol 217 (1) ◽  
pp. 53-74 ◽  
Author(s):  
Sergei Fedorov
Keyword(s):  
Hardy Space ◽  
Invariant Subspace ◽  
Connected Domain ◽  
Multiply Connected Domain ◽  
Multiply Connected

scholarly journals A Beurling Theorem for Generalized Hardy Spaces on a Multiply Connected Domain

2018 ◽  
Vol 70 (3) ◽  
pp. 515-537 ◽  
Author(s):  
Yanni Chen ◽  
Don Hadwin ◽  
Zhe Liu ◽  
Eric Nordgren
Keyword(s):  
Hardy Space ◽  
Connected Domain ◽  
Multiplication Operators ◽  
Multiply Connected Domain ◽  
Multiply Connected ◽  
Subspace Theorem ◽  
Cyclic Vectors ◽  
Generalized Hardy Spaces ◽  
Space Case ◽  
Beurling Theorem

AbstractThe object of this paper is to prove a version of the Beurling–Helson–Lowdenslager invariant subspace theorem for operators on certain Banach spaces of functions on a multiply connected domain in ℂ. The norms for these spaces are either the usual Lebesgue and Hardy space norms or certain continuous gauge norms. In the Hardy space case the expected corollaries include the characterization of the cyclic vectors as the outer functions in this context, a demonstration that the set of analytic multiplication operators is maximal abelian and reflexive, and a determination of the closed operators that commute with all analytic multiplication operators.

Construction of complex potentials for multiply connected domain

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Pyotr N. Ivanshin
Keyword(s):  
Integral Equation ◽  
Analytic Function ◽  
Linear System ◽  
Unbounded Domain ◽  
Connected Domain ◽  
Complex Potential ◽  
Cauchy Integral ◽  
Multiply Connected Domain ◽  
Multiply Connected ◽  
Impermeable Boundary

AbstractThe method of reduction of a Fredholm integral equation to the linear system is generalized to construction of a complex potential – an analytic function in an unbounded multiply connected domain with a simple pole at infinity which maps the domain onto a plane with horizontal slits. We consider a locally sourceless, locally irrotational flow on an arbitrary given 𝑛-connected unbounded domain with impermeable boundary. The complex potential has the form of a Cauchy integral with one linear and 𝑛 logarithmic summands. The method is easily computable.

Sign in / Sign up

Export Citation Format

Share Document