Functions of bounded variation on compact subsets of the plane

Volume 169 / 2005

Brenden Ashton, Ian Doust Studia Mathematica 169 (2005), 163-188 MSC: 47B40, 26B30. DOI: 10.4064/sm169-2-5

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 ${\rm BV}(\sigma)$ 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.

Authors

  • Brenden AshtonSchool of Mathematics
    University of New South Wales
    Sydney, NSW 2036, Australia
    and
    CiSRA
    3 Thomas Holt Drive
    North Ryde, 2113, Australia
    e-mail
  • Ian DoustSchool of Mathematics
    University of New South Wales
    Sydney, NSW 2036, Australia
    e-mail

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