ON THE CONTINUITY OF THE MTH ROOT OF A CONTINUOUS NONNEGATIVE DEFINITE MATRIX-VALUED FUNCTION

Authors
CHEN ZZ HUAN ZD
Citation
Zz. Chen et Zd. Huan, ON THE CONTINUITY OF THE MTH ROOT OF A CONTINUOUS NONNEGATIVE DEFINITE MATRIX-VALUED FUNCTION, Journal of mathematical analysis and applications, 209(1), 1997, pp. 60-66
Citations number
5
Categorie Soggetti
Mathematics, Pure",Mathematics,Mathematics,Mathematics
Journal title
Journal of mathematical analysis and applications → ACNP
ISSN journal
0022247X
Volume
209
Issue
1
Year of publication
1997
Pages
60 - 66
Database
ISI
SICI code
0022-247X(1997)209:1<60:OTCOTM>2.0.ZU;2-V
Abstract
In this paper we prove that the mth root of a nonnegative definite mat rix-valued function with continuous entries is continuous. In particul ar, if all the entries are C-alpha for alpha is an element of (0, 2], the mth root is C-alpha/m, which generalizes the result on the square root with alpha = 2 by M. Friedlin (Probab. Theory Appl. 13, 1968, 375 -378). (C) 1997 Academic Press.