Geodesic
Functions of bounded variation on compact subsets of the plane
Brenden Ashton 1   ; Ian Doust 2
1 School of Mathematics University of New South Wales Sydney, NSW 2036, Australia and CiSRA 3 Thomas Holt Drive North Ryde, 2113, Australia
2 School of Mathematics University of New South Wales Sydney, NSW 2036, Australia
Studia Mathematica, Tome 169 (2005) no. 2, pp. 163-188 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 ${\rm BV}(\sigma)$ 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.
DOI : 10.4064/sm169-2-5
Keywords: major obstacle extending theory well bounded operators cover operators whose spectrum necessarily real has lack suitable variation norm applicable functions defined arbitrary nonempty compact subset nbsp sigma plane paper define banach algebra sigma functions bounded variation set function theoretic properties algebra make better suited applications spectral theory those previously

Brenden Ashton  1   ; Ian Doust  2

1 School of Mathematics University of New South Wales Sydney, NSW 2036, Australia and CiSRA 3 Thomas Holt Drive North Ryde, 2113, Australia
2 School of Mathematics University of New South Wales Sydney, NSW 2036, Australia 
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Brenden Ashton; Ian Doust. Functions of bounded variation on
 compact subsets of the plane. Studia Mathematica, Tome 169 (2005) no. 2, pp. 163-188. doi: 10.4064/sm169-2-5

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