Polar wavelets and associated Littlewood-Paley theory
Abstract We develop an almost orthogonal wavelet-type expansion in ℝ² which is adapted to polar coordinates. We start by defining a product Fourier-Hankel transform f̂ and proving a sampling formula for f such that f̂ is compactly supported. For general f, the sampling formula and a partition of unity lead to an identity of the form , in which each function and is concentrated near a certain annular sector, has compactly supported product Fourier-Hankel transform, and is smooth away from the...