Geodesic
A way of estimating the convergence rate of the Fourier method for PDE of hyperbolic type
Czechoslovak Mathematical Journal, Tome 51 (2001) no. 3, pp. 561-572.

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The Fourier expansion in eigenfunctions of a positive operator is studied with the help of abstract functions of this operator. The rate of convergence is estimated in terms of its eigenvalues, especially for uniform and absolute convergence. Some particular results are obtained for elliptic operators and hyperbolic equations.
Classification : 35L10, 35L90, 42C15, 47A60, 47A70, 47F05
Keywords: elliptic operators; eigenfunctions; Fourier series; hyperbolic equation 
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     author = {Pustylnik, Evgeniy},
     title = {A way of estimating the convergence rate of the {Fourier} method for {PDE} of hyperbolic type},
     journal = {Czechoslovak Mathematical Journal},
     pages = {561--572},
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     zbl = {1079.35527},
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     url = {http://geodesic.mathdoc.fr/item/CMJ_2001__51_3_a8/}
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Pustylnik, Evgeniy. A way of estimating the convergence rate of the Fourier method for PDE of hyperbolic type. Czechoslovak Mathematical Journal, Tome 51 (2001) no. 3, pp. 561-572. http://geodesic.mathdoc.fr/item/CMJ_2001__51_3_a8/