The Martin boundaries of equivalent sheaves

Taylor, John C.. "The Martin boundaries of equivalent sheaves." Annales de l'institut Fourier 20.1 (1970): 433-456. <http://eudml.org/doc/74008>.

@article{Taylor1970,
abstract = {The Martin compactification of $X$ defined by a Brelot sheaf $H_1$ satisfying proportionality is shown to be the same as for $H_2$ if the sheaves agree outside a compact set. Minimal points coincide and hence $S^+_1$ and $S^+_2$ are isomorphic topological cones. Nakai’s result on the extension to $X$ of a function harmonic outside a compact set is extended to Bauer’s theory. The connected components of the Martin boundary $\Delta $ correspond to the ends of $X$ which are related to direct decomposition of the cone $H^+$.},
author = {Taylor, John C.},
journal = {Annales de l'institut Fourier},
keywords = {partial differential equations},
language = {eng},
number = {1},
pages = {433-456},
publisher = {Association des Annales de l'Institut Fourier},
title = {The Martin boundaries of equivalent sheaves},
url = {http://eudml.org/doc/74008},
volume = {20},
year = {1970},
}

TY - JOUR
AU - Taylor, John C.
TI - The Martin boundaries of equivalent sheaves
JO - Annales de l'institut Fourier
PY - 1970
PB - Association des Annales de l'Institut Fourier
VL - 20
IS - 1
SP - 433
EP - 456
AB - The Martin compactification of $X$ defined by a Brelot sheaf $H_1$ satisfying proportionality is shown to be the same as for $H_2$ if the sheaves agree outside a compact set. Minimal points coincide and hence $S^+_1$ and $S^+_2$ are isomorphic topological cones. Nakai’s result on the extension to $X$ of a function harmonic outside a compact set is extended to Bauer’s theory. The connected components of the Martin boundary $\Delta $ correspond to the ends of $X$ which are related to direct decomposition of the cone $H^+$.
LA - eng
KW - partial differential equations
UR - http://eudml.org/doc/74008
ER -