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https://doi.org/10.1007/978-3-642-41461-9Let . be a bounded domain in ℂ. with piecewise smooth boundary .. Consider a function ƒ ε .(.) and a set . ⊂ . of positive Lebesgue measure and assume that the .( .(.))-convex hull of. does not contain the coordinate origin.Then there is a function . ∊ .(.(.)) such that .(0) = 1 and外面 发表于 2025-3-22 20:14:18
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https://doi.org/10.1007/978-3-642-41461-9The following classical assertion is well known. Let . be a bounded classical domain with smooth boundary ., and ƒ ∈ .(.). Then.for all functions . ∈ .(.) if and only if .(.) extends into the domain . as a holomorphic function of class .(.) (see, for example, ).Projection 发表于 2025-3-23 07:04:42
https://doi.org/10.1007/978-3-642-41461-9We state a result on the possibility of analytic continuation from a smooth curve Γ to a given circle (for example, the unit circle), which is close in meaning to the result by Fok-Kuni (see sec. 27, 4°), but can not be obtained from it by conformal mapping. It is simpler both in formulation and in manner of proving.