Analytic Extension of Functions from Analytic Hilbert Spaces*

Abstract

Let M be an invariant subspace of $H^{2}_{v} $. It is shown that for each f ∈ M ^⊥, f can be analytically extended across ∂${\partial \mathbb{B}_{d} } \mathord{\left/ {\vphantom {{\partial \mathbb{B}_{d} } {\sigma {\left( {S_{{z_{1} }} , \cdots ,S_{{z_{d} }} } \right)}}}} \right. \kern-\nulldelimiterspace} {\sigma {\left( {S_{{z_{1} }} , \cdots ,S_{{z_{d} }} } \right)}}.$

Keywords

Analytic Hilbert space / Spectrum / Analytic extension / 47B35 / 47B20

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