Undergraduate Course: Hilbert Spaces and Fourier Analysis (MATH10045)
Course Outline
| School |
School of Mathematics |
College |
College of Science and Engineering |
| Course type |
Standard |
Availability |
Available to all students |
| Credit level (Normal year taken) |
SCQF Level 10 (Year 4 Undergraduate) |
Credits |
20 |
| Home subject area |
Mathematics |
Other subject area |
Specialist Mathematics & Statistics (Honours) |
| Course website |
http://student.maths.ed.ac.uk
|
Taught in Gaelic? |
No |
| Course description |
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). |
Information for Visiting Students
| Pre-requisites |
None |
| Displayed in Visiting Students Prospectus? |
Yes |
Course Delivery Information
| Not being delivered |
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.
|
Assessment Information
Examination only.
|
Special Arrangements
| None |
Additional Information
| Academic description |
Not entered |
| Syllabus |
Not entered |
| Transferable skills |
Not entered |
| Reading list |
Not entered |
| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords |
HSFA |
Contacts
| Course organiser |
Dr Liam O'Carroll
Tel: (0131 6)50 5070
Email: L.O'Carroll@ed.ac.uk |
Course secretary |
Ms Jennifer Marshall
Tel: (0131 6)50 5048
Email: Jennifer.Marshall@ed.ac.uk |
|
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