×

A way of estimating the convergence rate of the Fourier method for PDE of hyperbolic type. (English) Zbl 1079.35527

Summary: 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.

MSC:

35L10 Second-order hyperbolic equations
42C15 General harmonic expansions, frames
47A60 Functional calculus for linear operators
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] E. I. Pustylnik: On functions of a positive operator. Mat. Sbornik 119 (1982), 32-37.
[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,
[3] E. I. Pustylnik: On optimal interpolation and some interpolation properties of Orlicz spaces. Dokl. Akad. Nauk SSSR 269 (1983), 292-295.
[4] C. Miranda: Partial Differential Equations of Elliptic Type. Springer-Verlag, Berlin, 1970. · Zbl 0198.14101
[5] E. Pustylnik: Functions of a second order elliptic operator in rearrangement invariant spaces. Integral Equations Operator Theory 22 (1995), 476-498. · Zbl 0837.46022 · doi:10.1007/BF01203387
[6] C. Bennett, R. Sharpley: Interpolation of Operators. Academic Press, Boston, 1988. · Zbl 0647.46057
[7] E. Pustylnik: Generalized potential type operators on rearrangement invariant spaces. Israel Math. Conf. Proc. 13 (1999), 161-171. · Zbl 0938.45010
[8] J. Peetre: Espaces d’interpolation et théorème de Soboleff. Ann. Inst. Fourier 16 (1966), 279-317. · Zbl 0151.17903 · doi:10.5802/aif.232
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.