Gäller från och med: Autumn 2019
Beslutad av: FN1/Anders Gustafsson
Datum för fastställande: 2013-11-15
Avdelning: Mathematics
Kurstyp: Gemensam kurs, avancerad nivå och forskarnivå
Kursen ges även på avancerad nivå med kurskoder: FMAN80, FMA260
Undervisningsspråk: English
Functional analysis and harmonic analysis are fundamental tools in many mathematical applications (e.g., in field theory, solid mechanics, control theory, signal processing) and in mathematical statistics and numerical analysis. The aim of the course is to convey knowledge about basic concepts and methods, and to give the ability, both to follow discussions where these are used and to independently solve mathematical problems which arise in the applications. An important goal of the course is also to develop a power of abstraction which makes it easier to see analogies between problems from apparently different fields.
Kunskap och förståelse
För godkänd kurs skall doktoranden
Färdighet och förmåga
För godkänd kurs skall doktoranden
Functional analysis: norms and approximation, completeness, compactness, function spaces, Hilbert spaces, orthogonality and orthogonal systems, linear operators, spectral theory. Dual spaces and Hahn-Banach. Harmonic analysis: the Fourier transform and Sobolev spaces. Uncertainty relations, the sampling theorem, Fourier transforms and analytic functions, the Hilbert transform.
Renardy, M. & Rogers, Robert C.: An Introduction to Partial Differential Equations. Springer, 2004. ISBN 9780387004440.
Some further material.
Undervisningsformer: Föreläsningar, övningar
Examinationsformer: Skriftlig tentamen, muntlig tentamen
Betygsskala: Underkänd, godkänd
Examinator:
Replaces FMA260F.
Kursansvariga:
Hemsida: http://www.maths.lth.se/course/funkharm/