Geodesic
Canonically Isomorphic Spaces of Bounded Solutions of △u = Pu
Canadian journal of mathematics, Tome 28 (1976) no. 2, pp. 446-448

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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. 
Glasner, Moses. Canonically Isomorphic Spaces of Bounded Solutions of △u = Pu. Canadian journal of mathematics, Tome 28 (1976) no. 2, pp. 446-448. doi: 10.4153/CJM-1976-045-4
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