AMOR
发表于 2025-3-27 00:40:16
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玷污
发表于 2025-3-27 01:36:49
Bounded Harmonic Functions,Liouville’s Theorem in complex analysis states that a bounded holo-morphic function on . is constant. A similar result holds for harmonic functions on ... The simple proof given below is taken from Edward Nelson’s paper , which is one of the rare mathematics papers not containing a single mathematical symbol.
brachial-plexus
发表于 2025-3-27 05:21:06
Positive Harmonic Functions,In Chapter 2 we proved that a bounded harmonic function on .. is constant. We now improve that result.
bizarre
发表于 2025-3-27 13:03:43
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迷住
发表于 2025-3-27 15:16:25
Harmonic Hardy Spaces,In Chapter 1 we defined the Poisson integral of a function . ∈ . to be the function . defined on . by ..
NEG
发表于 2025-3-27 18:47:16
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悲观
发表于 2025-3-27 23:47:49
Annular Regions,An . is a set of the form {. ∈ .. : .. < ∈. ∈ < ..}; here .. ∈ . Thus an annular region is the region between two concentric spheres, or is a punctured ball, or is the complement of a closed ball, or is ..{0}.
BAN
发表于 2025-3-28 04:12:35
Harmonic Functions on Half-Spaces,at on . One advantage of . over . is the dilation-invariance of . We have already put this to good use in the section . in Chapter 2. Some disadvantages: . is not compact and Lebesgue measure on . is not finite.
附录
发表于 2025-3-28 08:41:03
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平
发表于 2025-3-28 13:29:15
The Dirichlet Problem and Boundary Behavior,techniques we developed for the special domains . and . will thus not be available. Most of this chapter will concern the Dirichlet problem. In the last section, however, we will study a different kind of boundary behavior problem—the construction of harmonic functions on . that cannot be extended harmonically across any part of ∂Ω.