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Cowen-Douglas operators and analytic continuation (2505.05649v1)
Published 8 May 2025 in math.FA, math.CV, and math.SP
Abstract: In this paper, we study certain Banach spaces of analytic functions on which a left-invertible multiplication operator acts. It turns out that, under natural conditions, its left inverse is a Cowen-Douglas operator. We investigate how the analytic continuations of functions from an invariant subspace of this Cowen-Douglas operator relate to the spectrum of its restriction to that subspace.