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 Hardyβs result.References
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Additional Information
- Luis Daniel Abreu
- Affiliation: Department of Mathematics, Universidade de Coimbra, Coimbra, Portugal 3001-454
- Email: daniel@mat.uc.pt
- Received by editor(s): October 19, 2004
- Received by editor(s) in revised form: April 7, 2005
- Published electronically: March 23, 2006
- Additional Notes: Partial financial assistance from Centro de MatemΓ‘tica da Universidade de Coimbra
- Communicated by: Carmen C. Chicone
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 2695-2701
- MSC (2000): Primary 42C05, 33D45; Secondary 39A13
- DOI: https://doi.org/10.1090/S0002-9939-06-08285-2
- MathSciNet review: 2213749