Hilbert Spaces and Fourier Analysis (U03856)

? Credit Points : 20 ? SCQF Level : 10 ? Acronym : MAT-4-HSFA

Inner product spaces, geometric and metric properties of Hilbert spaces, orthogonal expansions and projections in Hilbert spaces. Bounded linear functionals and operators, compact operators on Hilbert spaces. The spectral theorem for selfadjoint compact operators.

Fourier series, pointwise convergence of Fourier series and other summability methods. Fourier transform, convolution, Schwartz spaces and tempered distributions, convergence and summability of Fourier integral, eigenfunctions of FT (Hermite polynomials).

Entry Requirements

? Pre-requisites : MAT-3-CVD, MAT-3-PAA

Subject Areas

Home subject area

Specialist Mathematics & Statistics (Honours), (School of Mathematics, Schedule P)

Delivery Information

? Normal year taken : 4th year

? Delivery Period : Full Year (Blocks 1-4)

? Contact Teaching Time : 2 hour(s) per week for 22 weeks

First Class Information

Date	Start	End	Room	Area	Additional Information
08/01/2008	12:10	13:00	Lecture Theatre 1, Ashworth Labs	KB

All of the following classes

Type	Day	Start	End	Area
Lecture	Tuesday	12:10	13:00	KB
Lecture	Friday	12:10	13:00	KB

? Additional Class Information : In S2 moves to M&Th at 1210 hrs

Summary of Intended Learning Outcomes

1. Ability to apply general theory to specific examples.
3. An ability to use orthogonality arguments in concrete situations.
4. Familiarity of basic functional/fourier analysis results and an ability to use them.
5. To gain an appreciation of the interplay between analysis, geometry and algebra in the setting of Hilbert spaces and Fourier theory.