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Representation of Complex Functions by Orthogonal Series and Faber Series the method of series expansions. The theory of convergence for functions defined on complex domains, especially for analytic functions, is considerably simpler than for functions defined on real domains. Since we are generally interested in analytic functions, we shall mainly be concerned with seriOTHER 发表于 2025-3-22 20:05:02
Approximation on Compact Setsf . is analytic on ., whereas a weakening of this assumption requires a much greater effort. We begin with Runge’s theorem; a weak version of it has already been proved, but the following proof will make Chapter III independent of the preceding chapters.lactic 发表于 2025-3-22 21:40:08
Approximation on Closed Setsshall approximate functions defined on a set . that is closed in a domain .. Functions analytic or meromorphic in . will serve as approximating functions. In the special case where . = ℂ, one obtains approximation by entire functions. Here the rate of approximation (as . → ∞) also plays a role. Seve业余爱好者 发表于 2025-3-23 03:57:31
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ic inhabitants with elongated, eel-shaped bodies and lack paired fins. Instead of jaws, lampreys possess a disc-shaped oral funnel armored with horny teeth. Their larvae, called ammocoetes, exhibit worm-like morphology without the orbits or the oral funnel. From their unique phylogenetic position wi