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
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.