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XVII.—Some Hyperspace Harmonic Analysis Problems introducing Extensions of Mathieu's Equation

Published online by Cambridge University Press:  15 September 2014

Pierre Humbert
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Extract

It is well known that two problems of harmonic analysis in ordinary three-dimensional space can be solved by Mathieu's functions, namely, (a) harmonic analysis for an orthogonal system of elliptic (or hyperbolic) cylinders,

(b) harmonic analysis for a system of confocal paraboloïds,

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 46 , 1927 , pp. 206 - 209
Copyright
Copyright © Royal Society of Edinburgh 1927

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References

page 206 note * Proc. Edin. Math. Soc., xl (1921–1922), p. 31Google Scholar.

page 208 note * For an account of the properties of Mathieu's associated functions,vide Ince, E L., Proc. Roy. Soc. Edin., xlii (1922)Google Scholar ; Proc. Edin. Math. Soc., xli (1922–1923)Google Scholar.

page 209 note * Analytical properties of this equation have been given by Whittaker, , Proc. Edin. Math. Soc., xxxiii (1914–1915)Google Scholar, and by Ince, E. L., Proc. London Math. Soc., xxiii (1923)Google Scholar.

page 209 note † This fact was pointed out to me by Mr E. T. Copson.