Lectures on complex analysis /
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...
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| Format: | eBook |
| Language: | English |
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Cham :
Springer,
2026.
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| Summary: | 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. |
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| Physical Description: | 1 online resource (xviii, 369 pages) : illustrations |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9783032139962 (electronic bk.) 3032139961 |