疏忽
发表于 2025-3-26 22:35:10
Conformal MappingsIn this chapter we consider a more global aspect of analytic functions, describing geometrically what their effect is on various regions. Especially important are the analytic isomorphisms and automorphisms of various regions, of which we consider many examples.
弯曲的人
发表于 2025-3-27 02:15:55
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Biofeedback
发表于 2025-3-27 05:17:32
The Riemann Mapping TheoremIn this chapter we give the general proof of the Riemann mapping theorem. We also prove a general result about the boundary behavior.
Conspiracy
发表于 2025-3-27 13:31:05
Applications of the Maximum Modulus Principle and Jensen’s FormulaWe return to the maximum principle in a systematic way, and give several ways to apply it, in various contexts.
Assault
发表于 2025-3-27 16:25:34
Elliptic FunctionsIn this chapter we give the classical example of entire and meromorphic functions of order 2. The theory illustrates most of the theorems proved so far in the book. A self-contained “analytic” continuation of the topics discussed in this chapter can be found in Chapters 3, 4, and 18 of my book on . .
invulnerable
发表于 2025-3-27 19:13:22
The Gamma and Zeta FunctionsWe now come to a situation where the natural way to define a function is not through a power series but through an integral depending on a parameter. We shall give a natural condition when we can differentiate under the integral sign, and we can then use Goursat’s theorem to conclude that the holomorphic function so defined is analytic.
乐章
发表于 2025-3-28 00:22:14
The Prime Number TheoremAt the turn of the century, Hadamard and de la Vallee Poussin independently gave a proof of the prime number theorem, exploiting the theory of entire functions which had been developed by Hadamard. Here we shall give D. J. Newman’s proof, which is much shorter. I have also benefited from Korevaar’s exposition.
平庸的人或物
发表于 2025-3-28 03:12:46
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角斗士
发表于 2025-3-28 08:32:12
https://doi.org/10.1007/978-3-540-26542-9rincipal ways will be by means of power series. Thus we shall see that the series.converges for all . to define a function which is equal to .. Similarly, we shall extend the values of sin . and cos . by their usual series to complex valued functions of a complex variable, and we shall see that they
Flat-Feet
发表于 2025-3-28 11:04:37
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