We regard the shearlet group as a semidirect product group and show that its standard representation is,typically, a quasiregu- lar representation. As a result we can characterize irreducible as well as square-integrable subrepresentations of the shearlet group.

A bounded linear operator T on a complex Hilbert space H is irreducible if it has no reducing subspace other than the trivial ones (0) and H; it is strongly irreducible if every operator similar to T is irreducible. Equivalently, T is irreducible (resp. strongly irreducible) if the only projections (resp. idempotent operators) commuting with T are 0 and I. Since (strongly) irreducible operators...

Oxide reducibility is a central concept quantifying the role of support in catalysis. While reducible oxides are often considered catalytically active, irreducible seen as inert supports. Enhancing has, however, emerged an effective way to increase their catalytic activity while retaining inherent thermal stability. In this work, we focus on prospect using single metal atoms prototypical oxide,...