数学物理学报（英文版）
數學物理學報（英文版）
수학물이학보（영문판）
ACTA MATHEMATICA SCIENTIA
2012年
2期
807-812
,共6页
Locally compact group%unitary representation%continuous frame%wavelet transform%direct integral
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 that 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.
