International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 1, Pages 61-74

Localization and summability of multiple Hermite series

G. E. Karadzhov and E. E. El-Adad

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 Rn are investigated by the Riesz summability method of order α>(n1)/2. 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 n-dimensional case. In particular, for these classes of functions the localization principle and summability on the Lebesgue set are established.