Gibbs’ phenomenon in higher dimensions

Abstract

Gibbs' phenomenon occurs for most orthogonal wavelet expansions in one dimension. It also exists in higher dimensions but fundamental concepts must be redefined. This is done for both separable and nonseparable wavelet expansions in severable variables.

Constructive Approximation of Discontinuous Functions by Neural Networks

“…The Gibbs phenomenon also appears in higher dimensions, for example, in the case of multiple Fourier series and integrals [6,18] and in multidimensional wavelet expansions [30].…”