Modular filter convergence theorems for abstract sampling type operators

Abstract

We study the problem of approximating a real-valued function f by considering sequences of general operators of sampling type, which include both discrete and integral ones. This approach gives a unitary treatment of various kinds of classical operators, such as Urysohn integral operators, in particular convolution integrals, and generalized sampling series.

Keywords:

• filter convergence
• filter exhaustiveness
• filter convergence in measure
• integral operator
• sampling series
• modular
• modular convergence
• filter singularity

AMS Subject Classifications::

• 41A25
• 41A35
• 46E30
• 47G10