Numerical Solvability and Solution of an Inverse Problem Related to the Gibbs Phenomenon. (14th June 2015) - Haidar, Nassar H. S.
Abstract : We report on the inverse problem for the truncated Fourier series representation off x ∈ BV - L, L in a form with a quadratic degeneracy, revealing the existence of the Gibbs-Wilbraham phenomenon. A new distribution-theoretic proof is proposed for this phenomenon. The paper studies moreover the iterative numerical solvability and solution of this inverse problem near discontinuities off x .