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The Space of Dirichlet-Finite Solutions of the Equation Δu = Pu on a Riemann Surface

Published online by Cambridge University Press:  22 January 2016

Mitsuru Nakai
Mitsuru Nakai*
Affiliation:
Mathematical Institute, Nagoya University
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Let R be an open Riemann surface. By a density P on R we mean a non-negative and continuously differentiable functions P(z) of local parameters z = x + iy such that the expression P(z)dxdy is invariant under the change of local parameters z. In this paper we always assume that P≢0 unless the contrary is explicitly mentioned. We consider an elliptic partial differential equation

which is invariantly defined on R.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 18 , April 1961 , pp. 111 - 131
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1961

References

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