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Canonically Isomorphic Spaces of Bounded Solutions of △u = Pu

Published online by Cambridge University Press:  20 November 2018

Moses Glasner
Moses Glasner*
Affiliation:
The Pennsylvania State University, University Park, Pennsylvania
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Let R be a hyperbolic Riemann surface and P, Q nonnegative C1 2-forms on R. The space of bounded solutions of △u = Pu (△u = Qu, respectively) on R is denoted by PB(R) (QB(R), respectively). A vector space isomorphism S between PB(R) and QB(R) is called canonical if for each u ϵ PB(R), there is a potential pu on R with \u — Su\ ≦ pu. The canonical isomorphism theme in the study of the equation △u = Pu was introduced in H. Royden's paper [9] on the order comparison condition.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 2 , 01 April 1976 , pp. 446 - 448
Copyright
Copyright © Canadian Mathematical Society 1976

References

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