منابع مشابه
Harmonic Functions in the Unit Disk
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متن کاملThe Inner Mapping Radius of Harmonic Mappings of the Unit Disk
The class SH consists of univalent, harmonic, and sense-preserving functions f in the unit disk, ∆, such that f = h + g where h(z) = z + ∑∞ 2 akz , g(z) = ∑∞ 1 bkz . Using a technique from Clunie and Sheil-Small, we construct a family of 1-slit mappings in SH by varying ω(z) = g ′(z)/f ′(z). As ω(z) changes, the tip of the slit slides along the negative real axis from the point 0 to −1. In doin...
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Our main result is to give necessary and sufficient conditions, in terms of Fourier transforms, on a closed ideal I in L1(G//K) , the space of radial integrable functions on G = SU(1 , 1) , so that I = L1(G//K) or I = L0(G//K)—the ideal of L 1(G//K) functions whose integral is zero. This is then used to prove a generalization of Furstenberg’s theorem which characterizes harmonic functions on th...
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Our main result is to give necessary and sufficient conditions, in terms of Fourier transforms, on a closed ideal / in Ll(G//K), the space of radial integrable functions on G = SU{1, 1), so that / = Ll(G//K) or / = L^(G//K)—the ideal of Ll(G//K) functions whose integral is zero. This is then used to prove a generalization of Furstenberg's theorem which characterizes harmonic functions on the un...
متن کاملHarmonic and Superharmonic Majorants on the Disk
We prove that a positive function on the unit disk admits a harmonic majorant if and only if a certain explicit upper envelope of it admits a superharmonic majorant. We provide examples to show that mere superharmonicity of the data does not help with the problem of existence of a harmonic majorant. 1. Definitions and statements Let D stand for the open unit disk in the complex plane, and H(D) ...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1999
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(99)00019-9