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Functions of bounded variation on compact subsets of the plane

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Ashton B., Doust I.

Studia Mathematica

2005

tom 169

nr 2

163-188

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.

Ograniczanie wyników

1 Studia Mathematica

1 Ashton B.

1 Doust I.

1 2005

Wyniki wyszukiwania

Functions of bounded variation on compact subsets of the plane