Prolate Spheroidal Wavelets in Higher Dimensions
Gilbert G. Walter · Journal of Integral Equations and Applications · 2006
Prolate spheroidal wavelets (PS wavelets) based on the first prolate spheroidal wave function (PSWF), were recently introduced.They were shown to have many desirable properties lacking in other wavelets.In particular, the subspaces belonging to the associated MRA were shown to be closed under differentiation and translation.In this paper, we introduce prolate spheroidal wavelets in higher dimensions.They are similar to the one-dimensional versions in that they are based on an eigenfunction of an integral operator.But there is not, in general, an associated differential operator which is helpful in the one dimensional case for construction.Hence another method of construction must be used.