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 on two-dimensional manifolds.
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Communicated by Gerald B. Folland
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Brandolini, L., Colzani, L. Localization and convergence of eigenfunction expansions. The Journal of Fourier Analysis and Applications 5, 431–447 (1999). https://doi.org/10.1007/BF01261637
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DOI: https://doi.org/10.1007/BF01261637