Functions of bounded variation on compact subsets of the plane

被引：16
|
作者：
Ashton, B
Doust, I
机构：
[1] CiSRA, N Ryde, NSW 2113, Australia
[2] Univ New S Wales, Sch Math, Sydney, NSW 2036, Australia
来源：
STUDIA MATHEMATICA | 2005年 / 169卷 / 02期
关键词：
functions of bounded variation; absolutely continuous functions; functional calculus; well-bounded operators; AC-operators;
D O I：
10.4064/sm169-2-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：163 / 188
页数：26
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