Comparison theorems for bounded solutions of \triangle𝑢=𝑃𝑢

Glasner, Moses

doi:10.1090/S0002-9947-1975-0377088-X

Comparison theorems for bounded solutions of $\triangle u=Pu$
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by Moses Glasner

Trans. Amer. Math. Soc. 202 (1975), 173-179

DOI: https://doi.org/10.1090/S0002-9947-1975-0377088-X

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Abstract:

Let $P$ and $Q$ be ${C^1}$ densities on a hyperbolic Riemann surface $R$. A characterization of isomorphisms between the spaces of bounded solutions of $\Delta u = Pu$ and $\Delta u = Qu$ on $R$ in terms of the Wiener harmonic boundary is given.

References

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