Orthogonality of Certain Functions with Respect to Complex Valued Weights
- 1 October 1981
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 33 (5) , 1261-1270
- https://doi.org/10.4153/cjm-1981-095-3
Abstract
In his work on the Dirichlet problem for the Heisenberg group Greiner [5] showed that each Lα-spherical harmonic is a unique linear combination of functions of the form with k = 0, 1,2, … and n = 0, ±l, ±2 , …, where Hk(α, n)(θiθ) is defined by the generating function Since Hk(0,0)(eiθ) = Pk(cos θ), where Pk(x) is the Legendre polynomial of degree k, and these functions satisfy the orthogonality relation Greiner raised the question of whether the functions Hk(0,0)(eiθ) are orthogonal or biorthogonal with respect to some complex valued weight function.Keywords
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