Wavelet frame characterization of Besov Spaces on stratified Lie groups

Abstract: Motivated by our construction of the Mexican hat wavelet on the Heisenberg group, we shall study and construct smooth continuous wavelets of higher vanishing moments on stratified Lie groups. We shall also study the circumstances under which our wavelets can be discretized into "nearly tight" frames. This is done by use of a discrete version of Calderon's reproducing formula, which we have obtained jointly with D. Geller. This formula has many other applications as well. We will conclude the talk with some applications of our wavelets (a joint work with H. F\"uhr), and some remarks and related questions on this topic.