Lectures on Complex Analysis

di Norbert Steinmetz (Autore)

Springer Nature Switzerland AG, 2026

This elegant textbook offers a comprehensive course on one-dimensional complex analysis. It includes many topics that, in this scope, are not covered in most other textbooks, such as a detailed investigation of the Schwarzian derivative and its associated differential equation, with applications to conformal mappings of circular polygons; various proofs of the uniformisation theorem for planar domains; an introduction to the theory of ordinary differential equations in the complex domain, culminating in a proof of the Cauchy–Kovalevskaya theorem; an introduction to the theory of normal families, including Zalcman's lemma; a proof of the Paley–Wiener theorem; a complete discussion of the Laguerre–Pólya class; solution of the Dirichlet problem, with special emphasis on harmonic measure and Green's function, and applications to conformal mappings of multiply connected domains; a detailed description of the dynamics of polynomials; and the consistent use of the theory of proper mappings whenever possible.

• Autore: Norbert Steinmetz
• Editore: Springer Nature Switzerland AG
• Anno: 2026
• Rilegatura: Hardback
• Pagine: 369 p.
• Dimensioni: 235 x 155 mm
• EAN: 9783032139955

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