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 |
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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). |
Course Delivery Information
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.
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Assessment Information
Examination only.
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Please see Visiting Student Prospectus website for Visiting Student Assessment information |
Special Arrangements
Not entered |
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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copyright 2010 The University of Edinburgh -
1 September 2010 6:18 am
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