# School of Mathematics

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### MA342A:2
Functional Analysis I

## Tutorial and exercise sheets

- Tutorial Sheet 1 [October 4]
- Examples and Fourier coefficients on $[0,1]$.
- Tutorial Sheet 2 [October 11]
- Dual groups and characters.
- Tutorial Sheet 3 [October 18]
- Sums of characters. Direct sums and their characters.
- Tutorial Sheet 4 [October 25]
- Examples of Fourier transforms on finite groups and on $\mathbb R$.
- Tutorial Sheet 5 [November 1]
- Examples of partial sums of Fourier series. Convolution example. Fourier coefficients of a convolution.
- Tutorial Sheet 6 [November 15]
- Translates (of functions). $C(\mathbb T ) \subseteq L^1(\mathbb T)$.
- Tutorial Sheet 7 [November 22]
- Homogeneous Banach space of functions, convoutions as vector-valued integrals.
- Tutorial/homwork Sheet 8 [due December 13]
- Solutions.