Functions 𝑞-orthogonal with respect to their own zeros

Abreu, Luis

doi:10.1090/S0002-9939-06-08285-2

Functions $q$-orthogonal with respect to their own zeros
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by Luis Daniel Abreu PDF

Proc. Amer. Math. Soc. 134 (2006), 2695-2701 Request permission

Abstract:

In 1939, G. H. Hardy proved that, under certain conditions, the only functions satisfying \begin{equation*} \int _{0}^{1}f(\lambda _{m}t)f(\lambda _{n}t)dt=0, \end{equation*} where the $\lambda _{n}$ are the zeros of $f$, are the Bessel functions. We replace the above integral by the Jackson $q$-integral and give the $q$-analogue of Hardy’s result.

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