Ian Doust's information pages

Functions of bounded variation on compact subsets of the plane

Brenden Ashton and Ian Doust

Studia Math., 169 (2005), 163-188.

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

Email:  i.doust@unsw.edu.au

Abstract: A major obstacle in extending the theory of well-bounded operators to cover operators whose spectrum is not necessarily real has been the lack of a suitable variation norm applicable to functions defined on an arbitrary nonempty compact subset $\sigma$ of the plane. In this paper we define a new Banach algebra $BV(\sigma)$ of functions of bounded variation on such a set and show that the function theoretic properties of this algebra make it better suited to applications in spectral theory than those used previously.

Note: The final version of the paper may differ from the manuscript below.
The manuscript is available in several forms: A comparison of how the operator theory that comes from these definitions compares to the more traditional ones can be found in the companion paper A comparison of algebras of functions of bounded variation.

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