Rappresentazioni di gruppi di Lie compatti ed equazioni alle derivate parziali

This work will study representation theory on compact Lie groups and the decomposition of the space of square-integrable functions with respect to the Haar measure. After proving that this decomposition is the spectral decomposition of the Laplace operator on the group SU(2), this work will use these results in order to study the heat equation on the group. In particular, it will solve the Cauchy problem with a Dirac delta function as the initial data.