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Gogoladze, L. , On the exponential uniform strong summability of multiple trigonometric Fourier series, Georgian Math. J. , 16 (2009), 517–532. MR 2572672 ( 2010k :42016) Gogoladze L
Density estimates with methods of uniform distribution mod 1. Some nonparametric multivariate density estimators for continuous functions, based on the Fejér and Jackson kernel, are presented. Uniform strong consistency results are obtained with methods of uniform distribution mod 1.
Abstract
This paper investigates closure properties possessed by certain classes of finite subdirect products of prime rings. If ℳ is a special class of prime rings then the class ℳ∞ of all finite subdirect products of rings in ℳ is shown to be weakly special. A ring S is said to be a right tight extension [resp. tight extension] of a subring R if every nonzero right ideal [resp. right ideal and left ideal] of S meets R nontrivially. Every hereditary class of semiprime rings closed under tight extensions is weakly special. Each of the following conditions imposed on a semiprime ring yields a hereditary class closed under right tight extensions: ACC on right annihilators; finite right Goldie dimension; right Goldie. The class of all finite subdirect products of uniformly strongly prime rings is shown to be closed under tight extensions, answering a published question.
