Continuous wavelets on compact manifolds (Q2391121)

\textit{F. J. Narcowich}, \textit{P. Petrushev} and \textit{J. D. Ward} [SIAM J. Math. Anal. 38, No. 2, 574--594 (2006; Zbl 1143.42034)] constructed \(C^\infty\) tight frames on \({\mathcal S}^n\) using for this aim continuous wavelet technique (the Calderon formula, etc.). Generalizing that approach and adding some new ingredients related to spectral theory, the authors construct \(C^\infty\) continuous wavelets \(\{K_t\}_{t> 0}\) on a smooth oriented Riemannian manifold. For the case of the 2-torus and the ``Mexican hat'' situation, the authors present two explicite approximate formulas for \(K_t\) one near \(t=0\) and one near \(t=\infty\).