Singular inner functions and associated measures
type: Item
instance of: scholarly article
title: Singular inner functions and associated measures
zbMATH Open document ID: 0832.30026
author: Nand Lal
author: Harish Chandra
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1995-04-04T00:00:00Z
review text: Every inner function \(S\) without zeros in the unit disc \(D\) has a unique representation \(S(z) = \lambda \exp \{- \int_{|z |= 1} {e^{it} + z \over e^{it} - z} d \mu (t)\}\), where \(|\lambda |= 1\) and \(\mu\) is a finite positive measure singular with respect to Lebesgue measure. The authors find explicit characterisations (in terms of \(\mu)\) of the measure corresponding to \(\mu\) for the composition \(S \circ \varphi\) when \(\varphi\) is (a) an analytic endomorphism of \(\partial D\) or (b) a conformal map of \(D\) to itself.
Mathematics Subject Classification ID: 30E20
zbMATH DE Number: 740394
zbMATH Keywords: singular measure
zbMATH Keywords: inner function
reviewed by: David A. Brannan
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 740394