Revista Matemática Iberoamericana

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Volume 18, Issue 3, 2002, pp. 511–540
DOI: 10.4171/RMI/327

Published online: 2002-12-31

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

Keiji Izuchi[1]

(1) Niigata University, Japan

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 $H^\infty + C$.

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

Izuchi Keiji: Outer and inner vanishing measures and division in $H^\infty + C$. Rev. Mat. Iberoam. 18 (2002), 511-540. doi: 10.4171/RMI/327