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

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

Keiji Izuchi

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

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 $H^\infty + C$.

Primary Subjects: 46J15

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

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.rmi/1051544318
Mathematical Reviews number (MathSciNet): MR1954863
Zentralblatt MATH identifier: 1034.46046

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