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Title: A way of estimating the convergence rate of the Fourier method for PDE of hyperbolic type (English)
Author: Pustylnik, Evgeniy
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 51
Issue: 3
Year: 2001
Pages: 561-572
Summary lang: English
Category: math
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. (English)
Keyword: elliptic operators
Keyword: eigenfunctions
Keyword: Fourier series
Keyword: hyperbolic equation
MSC: 35L10
MSC: 35L90
MSC: 42C15
MSC: 47A60
MSC: 47A70
MSC: 47F05
idZBL: Zbl 1079.35527
idMR: MR1851547
Date available: 2009-09-24T10:45:08Z
Last updated: 2016-04-07
Stable URL:
Reference: [1] E. I.  Pustylnik: On functions of a positive operator.Mat. Sbornik 119 (1982), 32–37. (Russian) MR 0672408
Reference: [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.
Reference: [3] E. I.  Pustylnik: On optimal interpolation and some interpolation properties of Orlicz spaces.Dokl. Akad. Nauk SSSR 269 (1983), 292–295. (Russian) MR 0698510
Reference: [4] C.  Miranda: Partial Differential Equations of Elliptic Type.Springer-Verlag, Berlin, 1970. Zbl 0198.14101, MR 0284700
Reference: [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, MR 1343341, 10.1007/BF01203387
Reference: [6] C.  Bennett, R.  Sharpley: Interpolation of Operators.Academic Press, Boston, 1988. MR 0928802
Reference: [7] E.  Pustylnik: Generalized potential type operators on rearrangement invariant spaces.Israel Math. Conf. Proc. 13 (1999), 161–171. Zbl 0938.45010, MR 1707363
Reference: [8] J.  Peetre: Espaces d’interpolation et théorème de Soboleff.Ann. Inst. Fourier 16 (1966), 279–317. Zbl 0151.17903, MR 0221282, 10.5802/aif.232


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