Vol. 62, No. 2, 1976

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Ordered Gleason parts

Herbert Stanley Bear, Jr.

Vol. 62 (1976), No. 2, 337–349

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
Received: 6 August 1975
Published: 1 February 1976
Herbert Stanley Bear, Jr.