Ian Doust's information pages

A comparison of algebras of functions of bounded variation

Brenden Ashton and Ian Doust

Address: School of Mathematics, University of New South Wales, Sydney NSW 2052, Australia

Email:  i.doust@unsw.edu.au

Abstract: Motivated by problems in the spectral theory of linear operators the authors previously introduced a new concept of variation for functions defined on a nonempty compact subset of the plane. In this paper we examine the algebras of functions of bounded variation one obtains from these new definitions for the case where the underlying compact set is either a rectangle or the unit circle, and compare these algebras with the ones previously used by Berkson and Gillespie in their theories of $AC$-operators and trigonometrically well-bounded operators.

This paper is currently under review.
The manuscript is available in several forms: This is a companion paper to Functions of bounded variation on compact subsets of the plane.

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