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

Evgenii Pustylnik

Czechoslovak Mathematical Journal (2001)

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

Abstract

top
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.

How to cite

top

Pustylnik, 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

top
  1. On functions of a positive operator, Mat. Sbornik 119 (1982), 32–37. (Russian) (1982) MR0672408
  2. Integral Operators in Spaces of Summable Functions, Izd.  Nauka, Moscow, 1966, English transl. Noordhoff, Leyden, 1976. (1966) 
  3. On optimal interpolation and some interpolation properties of Orlicz spaces, Dokl. Akad. Nauk SSSR 269 (1983), 292–295. (Russian) (1983) MR0698510
  4. Partial Differential Equations of Elliptic Type, Springer-Verlag, Berlin, 1970. (1970) Zbl0198.14101MR0284700
  5. 10.1007/BF01203387, Integral Equations Operator Theory 22 (1995), 476–498. (1995) Zbl0837.46022MR1343341DOI10.1007/BF01203387
  6. Interpolation of Operators, Academic Press, Boston, 1988. (1988) MR0928802
  7. Generalized potential type operators on rearrangement invariant spaces, Israel Math. Conf. Proc. 13 (1999), 161–171. (1999) Zbl0938.45010MR1707363
  8. 10.5802/aif.232, Ann. Inst. Fourier 16 (1966), 279–317. (1966) Zbl0151.17903MR0221282DOI10.5802/aif.232

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.