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Triple orthogonal series

Published online by Cambridge University Press:  18 May 2009

Robert Feinerman
Robert Feinerman
Affiliation:
Department of Mathematics, Herbert H. Lehman College (CUNY), Bronx, New York 10468
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In a number of recent papers, we have developed an abstract approach to dual orthogonal series (see [1], [2], [3], and [4]). Such series arise in crack theory, heat transfer, etc. In this paper, we generalize these results to triple orthogonal series. We also show, via a counterexample, that, surprisingly, the results in the dual case are not generalizable as completely as expected.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 20 , Issue 1 , January 1979 , pp. 49 - 53
Copyright
Copyright © Glasgow Mathematical Journal Trust 1979

References

REFERENCES

1.Feinerman, R. and Kelman, R., The convergence of least squares approximations for dual orthogonal series, Glasgow Math. J. 15 (1974), 82–84 and Corrigenda, ibid 184.CrossRefGoogle Scholar
2.Kelman, R. and Feinerman, R., Dual orthogonal series, SIAM J. Math. Anal. 5 (1974), 489–502.CrossRefGoogle Scholar
3.Feinerman, R. and Kelman, R., Dual orthogonal series with oscillatory modifiers, SIAM J. Math. Anal. 9 (1978), 591–594.CrossRefGoogle Scholar
4.Feinerman, R., Dual orthogonal series with modifier tending to zero, SIAM J. Math. Anal. 9 (1978), 667–670.CrossRefGoogle Scholar
5.Bachman, G. and Narici, L., Functional analysis, (Academic Press, 1966).Google Scholar