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Selçuk Journal
of
Applied Mathematics
Summer-Autumn, 2000
Volume 1
Number 1
Research Center
of
Applied Mathematics
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SJAM
Summer-Autumn 2000, Volume 1 - Number 1
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Optimal cubature formulas for Fourier coefficients of periodic functions
in Sobolev spaces
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Haydar
Bulgak1, Vladimir Vaskevich2* |
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1
Research Centre of Applied Mathematics, Selçuk University, Konya,
Turkey
email:
hbulgak@selcuk.edu.tr
2
Sobolev Institute of Mathematics, SB RAS, Novosibirsk, Russia;
email: vask@math.nsc.ru
Received: August 03, 2000
To
Prof. Dr. Chr. Zenger 60-th birthday
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Summary
The purpose of the paper is to discuss methods for constructing weighted cubature formulas in Sobolev spaces with periodic members. These formulas are intended to approximate the calculation of Fourier coefficients of functions under consideration. The explicit formulas for the weights and the errors of optimal cubature formulas are obtained by techniques from functional analysis and partial differential equations.
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Key
words
Fourier coefficients, optimal cubature formulas, difference operators of Sobolev type, the error estimations, the Filon quadrature formula
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Mathematics Subject Classification (1991):
65D32,
65D30, 41A55
*
The research was financially supported by the Scientific and
Technical Research Council of Turkey (TUBITAK) in the framework of a
NATO-PC Advanced Fellowships Programme and by RFBR Grant No.
98-01-00760.
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Article
in PS format (174 kb) |
Article
in ZIP format (66 kb) |
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