Ridgelets and the Representation of Mutilated Sobolev Functions

Abstract

We show that ridgelets, a system introduced in [4], are optimal to represent smooth multivariate functions that may exhibit linear singularities. For instance, let {u · x− b > 0} be an arbitrary hyperplane and consider the singular function f(x) = 1{u·x−b>0}g(x), where g is compactly supported with finite Sobolev L2 norm ‖g‖Hs , s > 0. The ridgelet… (More)
DOI: 10.1137/S003614109936364X

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