Functions and Analysis

1308 Submissions

[3] viXra:1308.0105 [pdf] submitted on 2013-08-19 12:19:46

Some New Types of Filter Limit Theorems for Topological Group-Valued Measures

Authors: Antonio Boccuto, Xenofon Dimitriou
Comments: 6 Pages.

Some new types of limit theorems for topological group-valued measures are proved in the context of filter convergence for suitable classes of filters. We investigate some fundamental properties of topological group-valued measures. We consider also Schur-type theorems, using the sliding hump technique, and prove some convergence theorems in the particular case of positive measures. We deal with the notion of uniform filter exhaustiveness, by means of which we prove some theorems on existence of the limit measure, some other kinds of limit theorems and their equivalence, using known results on existence of countably additive restrictions of strongly bounded measures.
Category: Functions and Analysis

[2] viXra:1308.0096 [pdf] submitted on 2013-08-19 04:32:59

Rates of Approximation for General Sampling-Type Operators in the Setting of Filter Convergence

Authors: Antonio Boccuto, Xenofon Dimitriou
Comments: 5 Pages.

We investigate the order of approximation of a real-valued function by means of suitable families of sampling type operators, which include both discrete and integral ones. We give a unified approach, by means of which it is possible to consider several kinds of classical operators, for instance Urysohn integral operators, in particular Mellin-type convolution integrals, and generalized sampling series. We deal with filter convergence, and our results are proper extensions of the classical ones.
Category: Functions and Analysis

[1] viXra:1308.0017 [pdf] submitted on 2013-08-03 18:40:35

Triple Integrals and Trilinear Forms

Authors: Quentin Hampus Dawkings
Comments: 2 Pages.

We derive a formula for triple integrating trilinear forms.
Category: Functions and Analysis