Institute of Mathematics with Computer Center at the Bulgarian Academy of Sciences
The multiple Hermite series in R^n are investigated by the Riesz summability method of order a > (n — l)/2. More precisely, locally uniform equisummability theorems for some classes of functions are proved and sharp sufficient conditions are given. Thus the classical Szegö results are improved and extended to the n-dimensional case. In particular, for these classes of functions the localization principle and the convergence on the Lebesgue set are established.
[Karadzhov G. E.; Karadzhov Georgi Eremiev; Karadžov Georgi; Караджов Георги Е.]