# A way of estimating the convergence rate of the Fourier method for PDE of hyperbolic type

Czechoslovak Mathematical Journal (2001)

- Volume: 51, Issue: 3, page 561-572
- ISSN: 0011-4642

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topPustylnik, Evgenii. "A way of estimating the convergence rate of the Fourier method for PDE of hyperbolic type." Czechoslovak Mathematical Journal 51.3 (2001): 561-572. <http://eudml.org/doc/30655>.

@article{Pustylnik2001,

abstract = {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.},

author = {Pustylnik, Evgenii},

journal = {Czechoslovak Mathematical Journal},

keywords = {elliptic operators; eigenfunctions; Fourier series; hyperbolic equation; elliptic operators; eigenfunctions; Fourier series; hyperbolic equation},

language = {eng},

number = {3},

pages = {561-572},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {A way of estimating the convergence rate of the Fourier method for PDE of hyperbolic type},

url = {http://eudml.org/doc/30655},

volume = {51},

year = {2001},

}

TY - JOUR

AU - Pustylnik, Evgenii

TI - A way of estimating the convergence rate of the Fourier method for PDE of hyperbolic type

JO - Czechoslovak Mathematical Journal

PY - 2001

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 51

IS - 3

SP - 561

EP - 572

AB - 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.

LA - eng

KW - elliptic operators; eigenfunctions; Fourier series; hyperbolic equation; elliptic operators; eigenfunctions; Fourier series; hyperbolic equation

UR - http://eudml.org/doc/30655

ER -

## References

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- Interpolation of Operators, Academic Press, Boston, 1988. (1988) MR0928802
- Generalized potential type operators on rearrangement invariant spaces, Israel Math. Conf. Proc. 13 (1999), 161–171. (1999) Zbl0938.45010MR1707363
- 10.5802/aif.232, Ann. Inst. Fourier 16 (1966), 279–317. (1966) Zbl0151.17903MR0221282DOI10.5802/aif.232

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