Gibbs phenomenon and its removal for a class of orthogonal expansions
نویسنده
چکیده
We detail the Gibbs phenomenon and its resolution for the family of orthogonal expansions consisting of eigenfunctions of univariate polyharmonic operators equipped with homogeneous Dirichlet boundary conditions. As we establish, it is possible to completely describe this phenomenon, including determining exact values for the size of the overshoot near both the domain boundary and the interior discontinuities of the function. Next, we demonstrate how the Gibbs phenomenon can be removed from such expansions using a number of different techniques. As a by-product, we introduce a generalisation of the classical Lidstone polynomials.
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