Frames arising from irreducible solvable actions. I. (Q679536)

The author develops a unified method which produces explicit construction of frames with precise frame bounds. The method relies on the use of unitary irreducible representations of some solvable Lie groups. No assumption on the integrability or square-integrability is made. A large class of representations which occur in wavelet theory and time-frequency analysis falls into the scope of the suggested scheme. These include the affine group, the generalized Heisenberg groups, the shearlet groups and various solvable extensions of non-commutative nilpotent Lie groups. The results are formulated in the language of the corresponding Lie algebras.