ASTER
发表于 2025-3-26 22:49:23
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偏离
发表于 2025-3-27 05:12:19
Prerequisites and Preliminaries,ble to that fostered by books like S. , R. and L. , but by no means a mastery of the contents of these books. A junior or senior mathematics major at any good college or university nowadays should therefore be adequately equipped.
Cubicle
发表于 2025-3-27 07:46:38
,Polynomial and Rational Approximation—Runge Theory,l approximants are thus produced. They are a very powerful tool for investigating holomorphic functions: often a theorem is easy for polynomials and remains valid under local uniform convergence, hence its validity passes over to holomorphic unctions generally.
forbid
发表于 2025-3-27 09:32:54
Omitted Values and Normal Families,functions on a common domain, none of which has 0 or 1 in its range, if bounded at a point, is uniformly bounded in a neighborhood of that point. The compactness theorems of Chapter VII then come into play with astounding consequences. Of course “0” and “1” here are convenient normalizations: any two distinct complex numbers would serve as well.
不如屎壳郎
发表于 2025-3-27 14:26:05
https://doi.org/10.1007/978-3-662-28908-2ely, when the integral is path independent, a primitive can be manufactured by using an “indefinite” integral (see the proof of 2.11). Thus the corresponding fundamental theorem(s) in the plane affirm that certain integrals over closed paths are 0.
假
发表于 2025-3-27 21:39:05
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大吃大喝
发表于 2025-3-27 23:40:40
,Erratum to: Schwarz’ Lemma and its Many Applications,
Heresy
发表于 2025-3-28 04:08:42
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transplantation
发表于 2025-3-28 09:58:45
Prerequisites and Preliminaries,t without proof I will attempt to state fully below with references. What is really expected of the reader is a level of mathematical maturity comparable to that fostered by books like S. , R. and L. , but by no means a mastery of the contents of these books. A junior or senior ma
essential-fats
发表于 2025-3-28 11:55:14
Curves, Connectedness and Convexity,l in all that follows. A deeper exploration of the topology of the plane occurs in Chapter IV, after the exponential function has been developed (in Chapter III) and the useful concept of the index of a curve is available.