Continuous frame wavelets

Let π be a unitary representation of a locally compact topological group G on a separable Hilbert space H. A vector ψ ∈ H is called a continuous frame wavelet if there exist A,B > 0 such thatA||φ||2∫G|〈π(g)ψ,φ〉|2dg≤B||φ||2(φ∈H),A||φ||2∫G|〈π(g)ψ,φ〉|2dg≤B||φ||2(φ∈H),in which dg is the left Haar measure of G. Similar to the study of wavelets, an essential problem in the study of continuous frame wavelets is how to characterize them under the given unitary representation. Moreover, we investigate a relation between admissible vectors of π and its components.