Wavelet analysis on some surfaces of revolution via area preserving projection
Let \(\mathcal{M}\) be a surface of revolution such that \(\mathcal{M}\) is generated by a smooth curve with infinite length rotating along the \(z\)-axis. Using a simple idea, the author constructs in section 2.1 an area-preserving projection from \(\mathcal{M}\) to (a subset of) the plane \(\mathbb{R}^2\). Three concrete examples are given with an explicit expression of the projection in sections 2.2, 2.3, and 2.4 for the paraboloid, hyperboloid, and conical surface, respectively. Due to the area preserving property of the projection, now any wavelet on the plane \(\mathbb{R}^2\) can be straightforwardly transformed into a corresponding wavelet on the surface \(\mathcal{M}\) of revolution. Consequently, this paper provides a simple way for constructing wavelets on surfaces of revolution generated by a smooth curve with infinite length.
scientific article; zbMATH DE number 5862782
scientific article