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
相关论文
共 17 条
  • [1] AMBROSIO L, 1989, B UNIONE MAT ITAL, V3B, P857
  • [2] ASHTON B, AC BETA OPERATORS
  • [3] Ashton B., 2000, THESIS U NEW S WALES
  • [4] ASHTON B, UNPUB COMP ALGEBRAS
  • [5] BENZINGER H, 1983, T AM MATH SOC, V275, P431
  • [6] ABSOLUTELY CONTINUOUS-FUNCTIONS OF 2 VARIABLES AND WELL-BOUNDED OPERATORS
    BERKSON, E
    GILLESPIE, TA
    [J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1984, 30 (OCT): : 305 - 321
  • [7] BERKSON E, 1985, J OPERAT THEOR, V13, P33
  • [8] BERKSON E, 1997, ACTA SCI MATH SZEGED, V6, P249
  • [9] On definitions of bounded variation for functions of two variables
    Clarkson, James A.
    Adams, C. Raymond
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1933, 35 (1-4) : 824 - 854
  • [10] Dowson, 1978, LONDON MATH SOC MONO, V12
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