2008
DOI: 10.1007/bf03321709
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The Structure of Certain Spaces of Analytic Functions

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Cited by 12 publications
(23 citation statements)
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“…• zf β ⊥ P (the collection of analytic polynomials) and zgβ ⊥ P, [4], [5] and [6]. In this section we present an alternate route to boundary values that has extension to the context of mean rational approximation.…”
Section: Boundary Values and Invariant Subspacesmentioning
confidence: 99%
See 1 more Smart Citation
“…• zf β ⊥ P (the collection of analytic polynomials) and zgβ ⊥ P, [4], [5] and [6]. In this section we present an alternate route to boundary values that has extension to the context of mean rational approximation.…”
Section: Boundary Values and Invariant Subspacesmentioning
confidence: 99%
“…The proof is excellent but complicated, and it does not really lend itself to showing the existence of nontangential boundary values in the case that spt(µ) ⊆ D, P t (µ) is irreducible and µ(T) > 0. X. Tolsa's remarkable results on analytic capacity opened the door for a new view of things, through the works of [4], [5] and [6]. In this section we present an alternate route to boundary values that has extension to the context of mean rational approximation.…”
Section: Boundary Values Another Waymentioning
confidence: 99%
“…Ui is the open set of analytic bounded point evaluations for P 2 (µ|∆ i ) for i ≥ 1, then Ui is a simply connected region and the closure of Ui contains ∆i. Conway and Elias (1993) extends some results of Thomson's Theorem to the space R 2 (K, µ), while Brennan (2008) expresses R 2 (K, µ) as a direct sum that includes both Thomson's theorem and results of Conway and Elias (1993). For a compactly supported complex Borel measure ν of C, by estimating analytic capacity of the set {λ : |Cν(λ)| ≥ c}, where Cν is the Cauchy transform of ν (see Section 3 for definition), Brennan (2006.…”
Section: Furthermore Ifmentioning
confidence: 57%
“…Furthermore, if Ui is the open set of analytic bounded point evaluations for P 2 (µ|∆ i ) for i ≥ 1, then Ui is a simply connected region and the closure of Ui contains ∆i. Conway and Elias (1993) extends some results of Thomson's Theorem to the space R 2 (K, µ), while Brennan (2008) expresses R 2 (K, µ) as a direct sum that includes both Thomson's theorem and results of Conway and Elias (1993). For a compactly supported complex Borel measure ν of C, by estimating analytic capacity of the set {λ : |Cν(λ)| ≥ c}, where Cν is the Cauchy transform of ν (see Section 2 for definition), Brennan (2006.…”
Section: Introductionmentioning
confidence: 57%