International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 1, Pages 61-74
Localization and summability of multiple Hermite series
Institute of Mathematics, Bulgarian Academy of Sciences, Sofia 1113, Bulgaria
Received 10 April 1995; Revised 5 October 1995
Copyright © 1997 G. E. Karadzhov and E. E. El-Adad. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The multiple Hermite series in are investigated by the Riesz summability
method of order . More precisely, localization theorems for some classes of functions
are proved and sharp sufficient conditions are given. Thus the classical Szegö results are extended
to the -dimensional case. In particular, for these classes of functions the localization principle
and summability on the Lebesgue set are established.