CYNIC
发表于 2025-3-21 17:17:56
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金桌活画面
发表于 2025-3-21 20:47:48
Properties of ,(G) and ,(G),, G is an open set in ℂ × ℂ = ℂ.. Then .(G) is defined just as in the one-variable case. (The distance in ℂ. between two points (z,w) and (z’,w’) will be denoted d((z,w), (z’,w’)) = (|z - z’|. + |w - w’|.).. We also define .(G) as before, but must first define ..
orient
发表于 2025-3-22 03:18:19
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Camouflage
发表于 2025-3-22 08:18:00
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Coeval
发表于 2025-3-22 12:13:33
The Cauchy Theorem,rectifiable curve γ: → ℂ, we let ‖γ‖ denote its length, i.e. ‖γ‖ = <Inline>1</Inline> |γ′(t)|dt, so that . where ‖f‖ = sup{| f(z) |: z ∈ γ}. The reader is reminded that γ^ denotes the “physical curve”, that is the image of γ.
Aprope
发表于 2025-3-22 16:31:00
Constructive Function Theory,n what follows, when we speak of a sequence of complex numbers we ordinarily mean a sequence with multiplicity, so that a function taking some value at a point of the sequence must take that value with the appropriate multiplicity. We also exclude the trivial function f ≡ 0 unless otherwise noted.
Aprope
发表于 2025-3-22 18:27:01
Ring (not Algebra) Isomorphisms of ,(G),s) = .(r) + .(s) for all r, s ∈ R.. A ring isomorphism is a ring homomorphism that is one-to-one and onto. If G and G’ are two conformally equivalent domains in ℂ then there is an algebra isomorphism from .(G) to .(G’) as we saw in Chapter 5. An algebra isomorphism will be a ring isomorphism which a
altruism
发表于 2025-3-22 23:13:17
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嘴唇可修剪
发表于 2025-3-23 04:52:50
Gap-Interpolation Theorems,nd interpolation are mixed. The idea is to take the Germay interpolation situation, where we want f(z.) = w., n = 1,2,3,… for some entire function f but now require that f have the form . where ⋀ is a given set of positive integers. For certain ⋀ (like ⋀ = ., the set of all positive integers), this
笨拙处理
发表于 2025-3-23 07:10:24
Textbook 1984m the point of view of functional analysis. The main object of study is the algebra H(G) of all holomorphic functions on the open set G, with the topology on H(G) of uniform convergence on compact subsets of G. From this point of vie~, the main theorem of the theory is Theorem 9.5, which concretely