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- W4238969547 abstract "Given a nonnegative ${C^1}$-function $p(x)$ on a Riemannian manifold $R$, denote by ${B_p}(R)$ the Banach space of all bounded ${C^2}$-solutions of $Delta u = pu$ with the sup-norm. The purpose of this paper is to give a unified treatment of ${B_p}(R)$ on the Wiener compactification for all densities $p(x)$. This approach not only generalizes classical results in the harmonic case $(p equiv 0)$, but it also enables one, for example, to easily compare the Banach space structure of the spaces ${B_p}(R)$ for various densities $p(x)$. Typically, let $beta (p)$ be the set of all $p$-potential nondensity points in the Wiener harmonic boundary $Delta$, and ${C_p}(Delta )$ the space of bounded continuous functions $f$ on $Delta$ with $f|Delta - beta (p) equiv 0$. Theorem." @default.
- W4238969547 created "2022-05-12" @default.
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- W4238969547 date "1974-03-01" @default.
- W4238969547 modified "2023-09-30" @default.
- W4238969547 title "Bounded solutions of the equation $Delta u=pu$ on a Riemannian manifold" @default.
- W4238969547 doi "https://doi.org/10.1090/s0002-9939-1974-0350654-8" @default.
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