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On the Gegenbauer transformation
Published online by Cambridge University Press: 14 November 2011
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