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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 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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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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/

[1] E. I.  Pustylnik: On functions of a positive operator. Mat. Sbornik 119 (1982), 32–37. (Russian) | MR

[2] M. A.  Krasnoselskii, P. P.  Zabreiko, E. I.  Pustylnik and P. E. Sobolevskii: Integral Operators in Spaces of Summable Functions. Izd.  Nauka, Moscow, 1966, English transl. Noordhoff, Leyden, 1976.

[3] E. I.  Pustylnik: On optimal interpolation and some interpolation properties of Orlicz spaces. Dokl. Akad. Nauk SSSR 269 (1983), 292–295. (Russian) | MR

[4] C.  Miranda: Partial Differential Equations of Elliptic Type. Springer-Verlag, Berlin, 1970. | MR | Zbl

[5] E.  Pustylnik: Functions of a second order elliptic operator in rearrangement invariant spaces. Integral Equations Operator Theory 22 (1995), 476–498. | DOI | MR | Zbl

[6] C.  Bennett, R.  Sharpley: Interpolation of Operators. Academic Press, Boston, 1988. | MR

[7] E.  Pustylnik: Generalized potential type operators on rearrangement invariant spaces. Israel Math. Conf. Proc. 13 (1999), 161–171. | MR | Zbl

[8] J.  Peetre: Espaces d’interpolation et théorème de Soboleff. Ann. Inst. Fourier 16 (1966), 279–317. | DOI | MR | Zbl