International Journal of Mathematics and Mathematical Sciences 
Volume 20 (1997), Issue 1, Pages 61-74
doi:10.1155/S0161171297000100

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

Abstract

The multiple Hermite series in Rn are investigated by the Riesz summability method of order α>(n−1)/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.