منابع مشابه
The Riemann Mapping Theorem
We will develop some of the basic concepts of complex function theory and prove a number of useful results concerning holomorphic functions. We will focus on derivatives, zeros, and sequences of holomorphic functions. This will lead to a brief discussion of the significance of biholomorphic mappings and allow us to prove the Riemann mapping theorem.
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The boundary of the Siegel disk of a quadratic polynomial with an irrationally indifferent fixed point with the golden mean rotation number has been observed to be self-similar. The geometry of this self-similarity is universal for a large class of holomorphic maps. A renormalization explanation of this universality has been proposed in the literature. However, one of the ingredients of this ex...
متن کاملThe Effective Riemann Mapping Theorem
The main results of the paper are two e ective versions of the Riemann mapping theorem. The rst, uniform version is based on the constructive proof of the Riemann mapping theorem by Bishop and Bridges and formulated in the computability framework developed by Kreitz and Weihrauch. It states which topological information precisely one needs about a nonempty, proper, open, connected, and simply c...
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The classical Riemann mapping theorem asserts that any topological quadrilateral in the complex plane can be mapped conformally onto a rectangle. The finite Riemann mapping theorem asserts that any topological quadrilateral tiled by finitely many 2-cells can be mapped with minimal combinatorial distortion onto a rectangle tiled by squares. We prove the finite Riemann mapping theorem, discuss it...
متن کاملA note on spectral mapping theorem
This paper aims to present the well-known spectral mapping theorem for multi-variable functions.
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1973
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1973.44.435