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The characteristic
function of a harmonic function in a locally Euclidean
space
William Lee Johnson |
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Vol. 23 (1967), No. 2, 291–297
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Abstract |
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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
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Milestones
Received: 1 December 1965
Revised: 12 October 1966
Published: 1 November 1967
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Authors |
| William Lee Johnson | |
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