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Trinity College Dublin

TCD Mathematics

School of Mathematics


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]