Admissible vectors for mock metaplectic representations

作者：De Mari Filippo; De Vito Ernesto^*

来源：Applied and Computational Harmonic Analysis, 2013, 34(2): 163-200.

DOI：10.1016/j.acha.2012.04.001

• Reproducing formula
• Wavelets
• Metaplectic representation

We obtain necessary and sufficient conditions for the admissible vectors of a new unitary non-irreducible representation U. The group G is an arbitrary semidirect product whose normal factor A is abelian and whose homogeneous factor H is a locally compact second countable group acting on a Riemannian manifold M. The key ingredient in the construction of U is a C-1 intertwining map between the actions of H on the dual group (A) over cap and on M. The representation U generalizes the restriction of the metaplectic representation to triangular subgroups of Sp(d,R), whence the name %26quot;mock metaplectic%26quot;. For simplicity, we content ourselves with the case where A = R-n and M = R-d. The main technical point is the decomposition of U as direct integral of its irreducible components. This theory is motivated by some recent developments in signal analysis, notably shearlets. Many related examples are discussed.

• 出版日期2013-3