Vol. 23, No. 2, 1967

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The characteristic function of a harmonic function in a locally Euclidean space

William Lee Johnson

Vol. 23 (1967), No. 2, 291–297

We define the characteristic function for each harmonic function having prescribed singularities in a locally Euclidean space and the class of harmonic functions with bounded characteristic. The main result is that any harmonic function of bounded characteristic can be represented as the difference of two positive harmonic functions with prescribed singularities. Thus the well-known theory of the characteristic functions associated with meromorphic functions has an analogue for harmonic functions in locally Euclidean spaces.

Mathematical Subject Classification
Primary: 31.11
Received: 1 December 1965
Revised: 12 October 1966
Published: 1 November 1967
William Lee Johnson