Tauberian type gap conditions for Cesàro summation methods

1999 ◽  
Vol 65 (1) ◽  
pp. 99-108
Author(s):  
S. A. Stepanyants
Keyword(s):  
Summation Methods ◽  
Tauberian Type

Summation methods and Lebesgue nonmeasurable functions

2017 ◽  
pp. 195-208
Author(s):  
Gilbert W. Bassett Jr. ◽  
Roger Koenker
Keyword(s):  
Summation Methods

Asymptotic normality of sums of Hilbert space valued random elements

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Alfredas Račkauskas
Keyword(s):  
Hilbert Space ◽  
Asymptotic Normality ◽  
Separable Hilbert Space ◽  
Linear Process ◽  
Weighted Sums ◽  
Bounded Operators ◽  
Linear Processes ◽  
Summation Methods ◽  
Random Elements

Abstract We investigate the asymptotic normality of distributions of the sequence {\sum_{k\in\mathbb{Z}}u_{n,k}X_{k}} , {n\in\mathbb{N}} , where {(X_{k},k\in\mathbb{Z})} either is a sequence of i.i.d. random elements or constitutes a linear process with i.i.d. innovations in a separable Hilbert space. The weights {(u_{n,k})} are in general a family of linear bounded operators. This model includes operator weighted sums of Hilbert space valued linear processes, operator-wise discounted sums in a Hilbert space as well some extensions of classical summation methods.

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