Mathematics: Complex Analysis 2

<p>This course is a continuation of Complex Analysis 1 and aims to provide a deeper understanding of fundamental concepts, results, and methods within the theory of analytic functions. It also develops the student's ability to apply this knowledge to describe, analyze, and solve relevant problems in complex analysis.</p><p>The course treats:</p> <ul> <li>Convergence of sequences of analytic functions. Locally uniform convergence, normal families, Montel’s theorem.</li> <li>In-depth study of conformal mappings. Riemann sphere, stereographic projection, Möbius transformations, disk automorphisms, Schwarz lemma, Riemann mapping theorem.</li> <li>Entire functions. Infinite products, factorization, order, genus. Fourier transforms and Paley-Wiener spaces.</li> <li>Harmonic and subharmonic functions. Maximum principle, Harnack’s principle, and application to Dirichlet’s problem in suitable domains.</li> </ul>