Revista Matemática Iberoamericana

Outer and inner vanishing measures and division in $H^\infty + C$

Keiji Izuchi

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Abstract

Measures on the unit circle are well studied from the view of Fourier analysis. In this paper, we investigate measures from the view of Poisson integrals and of divisibility of singular inner functions in $H^\infty + C$. Especially, we study singular measures which have outer and inner vanishing measures. It is given two decompositions of a singular positive measure. As applications, it is studied division theorems in $H^\infty + C$.

Article information

Source
Rev. Mat. Iberoamericana, Volume 18, Number 3 (2002), 511-540.

Dates
First available in Project Euclid: 28 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1051544318

Mathematical Reviews number (MathSciNet)
MR1954863

Zentralblatt MATH identifier
1034.46046

Subjects
Primary: 46J15: Banach algebras of differentiable or analytic functions, Hp-spaces [See also 30H10, 32A35, 32A37, 32A38, 42B30]

Keywords
Singular inner function bounded analytic function $H^\infty + C$

Citation

Izuchi, Keiji. Outer and inner vanishing measures and division in $H^\infty + C$. Rev. Mat. Iberoamericana 18 (2002), no. 3, 511--540. https://projecteuclid.org/euclid.rmi/1051544318


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