Functions of bounded variation on compact subsets of the plane

• Autorzy: Brenden Ashton , Ian Doust
• Języki publikacji: EN

Abstrakty

EN

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 σ of the plane. In this paper we define a new Banach algebra BV(σ) 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.

Kategorie tematyczne

• 26B30: Absolutely continuous functions, functions of bounded variation
• 47B40: Spectral operators, decomposable operators, well-bounded operators, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 169
• Numer: 2
• Strony: 163-188

Daty

wydano

2005

Twórcy

autor

Brenden Ashton

• School of Mathematics, University of New South Wales, Sydney, NSW 2036, Australia
• CiSRA, 3 Thomas Holt Drive, North Ryde, 2113, Australia

autor

Ian Doust

• School of Mathematics, University of New South Wales, Sydney, NSW 2036, Australia

Identyfikatory

DOI

10.4064/sm169-2-5