The Concept of a Riemann Surface
Courier Corporation, 31. des. 2013 - 208 sider
This classic on the general history of functions was written by one of the twentieth century's best-known mathematicians. Hermann Weyl, who worked with Einstein at Princeton, combined function theory and geometry in this high-level landmark work, forming a new branch of mathematics and the basis of the modern approach to analysis, geometry, and topology.
The author intended this book not only to develop the basic ideas of Riemann's theory of algebraic functions and their integrals but also to examine the related ideas and theorems with an unprecedented degree of rigor. Weyl's two-part treatment begins by defining the concept and topology of Riemann surfaces and concludes with an exploration of functions of Riemann surfaces. His teachings illustrate the role of Riemann surfaces as not only devices for visualizing the values of analytic functions but also as indispensable components of the theory.
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Abelian admissible local coordinate analytic continuation analytic form analytic function arbitrary associated boundary circle closed curve closed differential closed path closed Riemann surface coeﬂicients compact complex concept conformal maps constant contained continuously differentiable convergence coordinate system countable cover transformations deﬁned deﬁnition diﬂerential Dirichlet integral Dirichlet principle divisor domain equation equivalent Euclidean exists ﬁnd ﬁnite number ﬁrst kind ﬁxed point follows function element function f Funktionen given grad H. A. Schwarz harmonic function hence inequality inﬁnite integral function interior lattice linear transformation linearly independent Math meromorphic functions multiples neighborhood obtain open set open unit disc parameter perfect covering surface plane points pl poles positive number power series proof punched surface radius regular analytic regular elements representation Riemann surface Riemann-Roch theorem satisﬁes simply connected singularities speciﬁed sphere t-plane theorem topological map torus two-dimensional manifold uniform functions uniformizing variable vanishes Weierstrass zero