Continuous wavelets on compact manifolds

Continuous Wavelets on Compact Manifolds

Let M be a smooth compact oriented Riemannian manifold, and let ∆M be the Laplace-Beltrami operator on M. Say 0 6= f ∈ S(R), and that f(0) = 0. For t > 0, let Kt(x, y) denote the kernel of f(t∆M). We show that Kt is well-localized near the diagonal, in the sense that it satisfies estimates akin to those satisfied by the kernel of the convolution operator f(t∆) on R. We define continuous S-wavel...

wavelets on non-euclidean manifolds

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Finite Element Wavelets on Manifolds

Preprint No. 1199, Department of Mathematics, University of Utrecht, June 2001. Submitted to IMA J. Numer. Anal. We construct locally supported, continuous wavelets on manifolds Γ that are given as the closure of a disjoint union of general smooth parametric images of an n-simplex. The wavelets are proven to generate Riesz bases for Sobolev spaces Hs(Γ) when s ∈ (−1, 3 2 ), if not limited by th...

Surgery on Compact Manifolds

Fractal Dimension of Graphs of Typical Continuous Functions on Manifolds

If M is a compact Riemannian manifold then we show that for typical continuous function defined on M, the upper box dimension of  graph(f) is as big as possible and the lower box dimension of graph(f) is as small as possible.