Ordered Gleason parts

Herbert Stanley Bear, Jr.

Vol. 62 (1976), No. 2, 337–349

DOI: 10.2140/pjm.1976.62.337

Abstract

On the points of the domain of a function space we define a partial ordering which extends naturally to the Gleason parts. A general maximum principle and Harnack convergence theorem are proved in terms of the ordering, as well as an integral kernel representation for Dirichlet spaces. The results are applied to a space of solutions of the heat equation, and a space of solutions of the wave equation.

Mathematical Subject Classification 2000

Primary: 46E15

Secondary: 31B05

Milestones

Received: 6 August 1975

Published: 1 February 1976