Jubilee 2019

Ursula Molter

IMAS, Universidad de Buenos Aires and CONICET

Title:

Approximation by Group Invariant Subspaces

Abstract:

In this talk we will look at the structure and approximation properties of $\Gamma$-invariant spaces of $L^2(R)$, where $R$ is a second countable LCA group. The invariance is with respect to the action of $\Gamma$, a non commutative group in the form of a semidirect product of a discrete cocompact subgroup of $R$ and a group of automorphisms. This class includes in particular most of the crystallographic groups.

By defining a range function we are able to characterize the property of being invariant under the action of the crystal-group with a property of the range function.

We then show how these results can be applied to prove the existence and construction of a $\Gamma$-invariant subspace that best approximates a set of functional data in $L^2(R)$. This is very relevant in applications since in the euclidean case, $\Gamma$-invariant subspaces are invariant under rigid movements, a very sought feature in models for signal processing.


Back to Jubilee 2019 speakers
Back to Jubilee 2019 home