The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations

This book represents the first attempt at a unified picture for the presence of the Gibbs (or Gibbs-Wilbraham) phenomenon in applications, its analysis and the different methods of filtering it out. The analysis and filtering cover the familiar Gibbs phenomenon in Fourier series and integral representations of functions with jump discontinuities. In ad­ dition it will include other representations, such as general orthogonal series expansions, general integral transforms, splines approximat...