Geodesic
Triple orthogonal series
Glasgow mathematical journal, Tome 20 (1979) no. 1, pp. 49-53

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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. 
Feinerman, Robert. Triple orthogonal series. Glasgow mathematical journal, Tome 20 (1979) no. 1, pp. 49-53. doi: 10.1017/S0017089500003712
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[1] 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. Google Scholar | DOI

[2] 2.Kelman, R. and Feinerman, R., Dual orthogonal series, SIAM J. Math. Anal. 5 (1974), 489–502. Google Scholar | DOI

[3] 3.Feinerman, R. and Kelman, R., Dual orthogonal series with oscillatory modifiers, SIAM J. Math. Anal. 9 (1978), 591–594. Google Scholar | DOI

[4] 4.Feinerman, R., Dual orthogonal series with modifier tending to zero, SIAM J. Math. Anal. 9 (1978), 667–670. Google Scholar | DOI

[5] 5.Bachman, G. and Narici, L., Functional analysis, (Academic Press, 1966). Google Scholar

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