Continuous Wavelets and Frames on Stratified Lie Groups I

Continuous Wavelets and Frames on Stratified Lie Groups I

Let G be a stratified Lie group and L be the sub-Laplacian on G. Let 0 6= f ∈ S(R). We show that Lf(L)δ, the distribution kernel of the operator Lf(L), is an admissible function on G. We also show that, if ξf(ξ) satisfies Daubechies’ criterion, then Lf(L)δ generates a frame for any sufficiently fine lattice subgroup of G.

Continuous Action of Lie Groups on R and Frames

Wavelet and frames have become a widely used tool in mathematics, physics, and applied science during the last decade. In this article we discuss the construction of frames for L(R) using the action of closed subgroups H ⊂ GL(n,R) such that H has an open orbit O in R under the action (h, ω) 7→ (h) (ω). If H has the form ANR, where A is simply connected and abelian, N contains a co-compact discr...

Continuous Action of Lie Groups on ℝn and Frames

Recursive Moving Frames for Lie Pseudo-Groups

This paper introduces a new, fully recursive algorithm for computing moving frames and differential invariants of Lie pseudo-group actions. The recursive method avoids unwieldy symbolic expressions that complicate the treatment of large scale applications of the equivariant moving frame method. The development leads to novel results on partial moving frames, structure equations, and new differe...

Moving Frames for Lie Pseudo–Groups

We propose a new, constructive theory of moving frames for Lie pseudo-group actions on submanifolds. The moving frame provides an effective means for determining complete systems of differential invariants and invariant differential forms, classifying their syzygies and recurrence relations, and solving equivalence and symmetry problems arising in a broad range of applications. Mathematics subj...