Pure Maths Colloquium: Linear, invariant equations on manifolds with a group symmetry.
6 December 2010 17:15 in CM221
Given a manifold M on which a group G acts with compact quotient M/G, we discuss natural methods of solving equations Tu = f for T a linear, G-invariant operator acting in functions on M.
It turns out that there are appropriate generalizations of the classical Fredholm property corresponding to the situations in which G is discrete, unimodular Lie, and even nonunimodular Lie. Furthermore, generalizations of the classical Paley-Wiener theorem can be combined with these Fredholm properties to obtain fine existence and uniqueness results for the equation.
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