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elliptic operators; eigenfunctions; Fourier series; hyperbolic equation
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.
[1] E. I.  Pustylnik: On functions of a positive operator. Mat. Sbornik 119 (1982), 32–37. (Russian) MR 0672408
[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 0698510
[4] C.  Miranda: Partial Differential Equations of Elliptic Type. Springer-Verlag, Berlin, 1970. MR 0284700 | 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. DOI 10.1007/BF01203387 | MR 1343341 | Zbl 0837.46022
[6] C.  Bennett, R.  Sharpley: Interpolation of Operators. Academic Press, Boston, 1988. MR 0928802
[7] E.  Pustylnik: Generalized potential type operators on rearrangement invariant spaces. Israel Math. Conf. Proc. 13 (1999), 161–171. MR 1707363 | Zbl 0938.45010
[8] J.  Peetre: Espaces d’interpolation et théorème de Soboleff. Ann. Inst. Fourier 16 (1966), 279–317. DOI 10.5802/aif.232 | MR 0221282 | Zbl 0151.17903
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