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On the Gegenbauer transformation

Published online by Cambridge University Press:  14 November 2011

P. Heywood  and
P. G. Rooney
P. Heywood
Affiliation:
Department of Mathematics, University of Edinburgh, James Clerk Maxwell Building, The King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, Scotland, U.K.
P. G. Rooney
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario M5S 1A1, Canada
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Synopsis

The Gegenbauer transformation Gλk is defined for λ > −1/2, k = 0, 1, 2, …, by

where, if being the Gegenbauer polynomial of index λ and degree k, and L0k is the Tchebichef polynomial of degree k. The transformation is studied on the spaces Lµ, p denned by the norm

and its boundedness and range on these spaces is determined and inversion formulae are found.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 115 , Issue 1-2 , 1990 , pp. 151 - 166
Copyright
Copyright © Royal Society of Edinburgh 1990

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References

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