On the Carleman formula for a matrix ball
type: Item
instance of: scholarly article
title: On the Carleman formula for a matrix ball
zbMATH Open document ID: 0997.32006
author: S. Kosbergenov
published in: Russian Mathematics
publication date: 2001-03-01T00:00:00Z
review text: Let \(\mathfrak B\) be a matrix ball and \(\Delta\) is the boundary of the matrix ball. The Hardy space \(\mathcal H^1(\mathfrak B)\) is the space of holomorphic functions satisfying \[ \sup_{0<r<1} \int_\Delta |f(rZ)|d\sigma(Z) < \infty. \] Let \(E\) be a set of a positive measure \(\sigma\) on \(\Delta\). This paper shows the formula, called the Carleman formula, which reconstructs the value of the function \(f\) of the Hardy class \(\mathcal H^1(\mathfrak B)\) in the domain \(\mathfrak B\) by its radial boundary values onto the set \(E\). The author uses the properties of the Bergman, Szegö, and Poisson kernels for \(\mathfrak B\).
reviewed by: Jinkee Lee
Mathematics Subject Classification ID: 32A26
Mathematics Subject Classification ID: 32A35
zbMATH DE Number: 1541428
zbMATH Keywords: Carleman formula
zbMATH Keywords: matrix ball
zbMATH Keywords: Hardy space
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1541428