We state a localization principle for expansions in eigenfunctions of a self-adjoint second order elliptic operator and we prove an equiconvergence result between eigenfunction expansions and trigonometric expansions. We then study the Gibbs phenomenon for eigenfunction expansions of piecewise smooth functions an two-dimensional manifolds
Brandolini, L., Colzani, L. (1999). Localization and convergence of eigenfunction expansions. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 5(5), 431-447 [10.1007/BF01261637].
Localization and convergence of eigenfunction expansions
Colzani, L
1999
Abstract
We state a localization principle for expansions in eigenfunctions of a self-adjoint second order elliptic operator and we prove an equiconvergence result between eigenfunction expansions and trigonometric expansions. We then study the Gibbs phenomenon for eigenfunction expansions of piecewise smooth functions an two-dimensional manifolds
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