Functions of bounded variation on compact subsets of the plane

Brenden Ashton, and Ian Doust. "Functions of bounded variation on compact subsets of the plane." Studia Mathematica 169.2 (2005): 163-188. <http://eudml.org/doc/286381>.

@article{BrendenAshton2005,
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 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.},
author = {Brenden Ashton, Ian Doust},
journal = {Studia Mathematica},
keywords = {functions of bounded variation; absolutely continuous functions; functional calculus; well-bounded operators; AC-operators},
language = {eng},
number = {2},
pages = {163-188},
title = {Functions of bounded variation on compact subsets of the plane},
url = {http://eudml.org/doc/286381},
volume = {169},
year = {2005},
}

TY - JOUR
AU - Brenden Ashton
AU - Ian Doust
TI - Functions of bounded variation on compact subsets of the plane
JO - Studia Mathematica
PY - 2005
VL - 169
IS - 2
SP - 163
EP - 188
AB - 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.
LA - eng
KW - functions of bounded variation; absolutely continuous functions; functional calculus; well-bounded operators; AC-operators
UR - http://eudml.org/doc/286381
ER -