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Università degli Studi di Genova |
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Università degli Studi di Genova |
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Abstract: We study a unitary non irreducible representation U of a semidirect product G whose normal factor A is abelian and whose homogeneous factor H is a locally compact second countable group acting on a Riemannian manifold X. The key ingredient is a C^1 intertwining map between the actions of H on the dual group of A and X. The representation U generalizes the restriction of the metaplectic representation to triangular subgroups of Sp(d,R). For simplicity, we restrict ourselves to the case where A=R^n and X=R^d. We decompose U as a direct integral and obtain necessary and sufficient conditions for its admissible vectors. Many examples are given. Keywords: reproducing formula, metaplectic representation, shearlets, MSC: 22, 28, 43  |