Authors
Citation
J. Rosenblatt, NORM CONVERGENCE IN ERGODIC-THEORY AND THE BEHAVIOR OF FOURIER-TRANSFORMS, Canadian journal of mathematics, 46(1), 1994, pp. 184-199
Citations number
14
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
ISSN journal
0008414X
Volume
46
Issue
1
Year of publication
1994
Pages
184 - 199
Database
ISI
SICI code
0008-414X(1994)46:1<184:NCIEAT>2.0.ZU;2-3
Abstract
The L(p)-norm convergence of weighted averages mu(n)f in ergodic theor
y is equivalent to the pointwise convergence of the Fourier transforms
mu(n). If h(gamma) = lim(n-->infinity) mu(n)(gamma), then the behavio
r of h determines when the L(p)-norm limit of mu(n)f is integral f dm.
The nature of such limit functions h is the focus of this article.