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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

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


Author: Moses Glasner
Journal: Trans. Amer. Math. Soc. 202 (1975), 173-179
MSC: Primary 31C15; Secondary 30A48
DOI: https://doi.org/10.1090/S0002-9947-1975-0377088-X
MathSciNet review: 0377088
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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.


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DOI: https://doi.org/10.1090/S0002-9947-1975-0377088-X
Keywords: Solution of $ \Delta u = Pu$, Riemann surfaces, Green's function, maximum principle, Wiener harmonic boundary
Article copyright: © Copyright 1975 American Mathematical Society

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