The course is shared by Horia Cornean and Morten Grud Rasmussen.
ECTS: 5 ECTS-point.
Prerequisites: one should have previously followed Analysis 1 and 2 on MAT3 and MAT4, and Geometry on MAT5.
Content: Integration of positive measurable functions; the monotone and dominated convergence theorems. The Lebesgue measure on Rn and its invariance. Product-measure, Tonelli and Fubini theorems. Hölder and Minkowski inequalities; Lebesgue-spaces and their completeness. Approximation by smooth functions. Convolution and approximation of identity. Fourier series, Riesz-Fischer theorem; orthogonal expansions in Hilbert spaces. The Fourier transform and the inversion theorem; Plancherel's identity.
Exam: oral examination, with intern censorship.
Grade: Pass/fail
One should read the indicated material in advance, and try to solve the given exercises beforehand. The book is wonderful, but rather concise and difficult to read.
Walter Rudin: Real and Complex Analysis. McGraw-Hill Education, Third edition. 1987
H.D. Cornean: Noter om bl.a. Banach, Brouwer, Schauder, Kakutani fikspunktsætninger, Hairy Ball, Jordans kurvesætning, Nash ligevægtspunkt for endelige spil. (link)
H.D. Cornean: Notes for the course Operatorer i Hilbertrum (link)
Written by Horia Cornean.