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Svensk version

MAI0063: Complex analysis, 8 hp - Ph.D. course, spring 2012

Course leader: Lars Alexandersson

Literature: Mats Andersson, Topics in Complex Analysis, Springer, chapter 1, 2.1-2.2, 3.1-3.4, 4, 5.1-5.2

Content: Integral representations of analytic functions; power series expansions and residues; global Cauchy theorems. Conformal mappings; the Riemann sphere and projective space. Approximation with rationals; Mittag-Leffler's theorem and the inhomogeneous Cauchy-Riemann equation; analytic continuation; simply connected domains. Harmonic functions; subharmonic functions. Weierstrass' theorem; zeros and growth

Organization: Lectures and problem sessions. Presentations

Examination: Active participation in problem sessions. Assigned problems. Presentation of a topic related to the course

Prerequisites: Graduate courses in integration theory and functional analysis (specific details). Some undergraduate course in complex analysis

Schedule: In Kompakta rummet, unless otherwise stated. Problem sessions are marked * and presentations +

Vecka 3
Tis 17/1 10-12 - kap 1
Ons 18/1 08-10
Vecka 4
Tis 24/1 10-12
* Fre 27/1 13-16, Determinanten
Vecka 5
Tis 31/1 10-12 - kap 2
Ons 1/2 08-10
Vecka 6
* Fre 10/2 13-16, Determinanten
Vecka 7
Tis 14/2 10-12 - kap 3
Ons 15/2 08-11
Vecka 8
* Tor 23/2 08-11, Determinanten
Vecka 9
Tis 28/2 10-12 - kap 4
Ons 29/2 08-11
Vecka 10
-
Vecka 11
* Tis 13/3 13-16, Determinanten
Fre 16/3 08-10 - kap 5
Vecka 12
Fre 23/3 08-10
Vecka 13
* Tis 27/3 13-16, Åskådliga rummet
Vecka 14
-
Vecka 15
-
Vecka 16
+ Fre 20/4 08-10   Marcus Kardell: A. Univalent functions;   Andreas Rejbrand: B. Picard's theorems
Vecka 17
+ Fre 27/4 09-10   Michail Krimpogiannis: E. Boundary values of harmonic functions
Vecka 18
+ Fre 4/5 08-10   Jonna Gill: C. Analytic functionals and the Fourier-Laplace transform;   Anna Orlof: D. Mergelyan's theorem

Senast uppdaterad: 2019-11-29