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Canonical isomorphisms of energy finite solutions of Δu = Pu on open Riemann surfaces

Published online by Cambridge University Press:  22 January 2016

Mitsuru Nakai
Mitsuru Nakai*
Affiliation:
Nagoya University
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We call a second order differential P(z)dxdy on a Riemann surface R a density if it is not identically zero and P(z) is a nonnegative Hölder continuous function of the local parameter z = x + iy in each parametric disk. To each density P on R we associate the linear space P(R) of C2 solutions of the equation Δu(z) = P(z)u(z) invariantly defined on R. We also consider subspaces PX(R) of P(R) consisting of solutions with certain boundedness properties X.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 56 , January 1975 , pp. 79 - 84
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1975

References

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