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Functions  -orthogonal with respect to their own zeros
Author(s):
Luis
Daniel
Abreu
Journal:
Proc. Amer. Math. Soc.
134
(2006),
2695-2701.
MSC (2000):
Primary 42C05, 33D45;
Secondary 39A13
Posted:
March 23, 2006
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Additional information
Abstract:
In 1939, G. H. Hardy proved that, under certain conditions, the only functions satisfying where the  are the zeros of  , are the Bessel functions. We replace the above integral by the Jackson  -integral and give the  -analogue of Hardy's result.
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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
DOI:
10.1090/S0002-9939-06-08285-2
PII:
S 0002-9939(06)08285-2
Keywords:
$q$-difference equations,
$q$-Bessel functions,
$q$-integral.
Received by editor(s):
October 19, 2004
Received by editor(s) in revised form:
April 7, 2005
Posted:
March 23, 2006
Additional Notes:
Partial financial assistance from Centro de Matemática da Universidade de Coimbra
Communicated by:
Carmen C. Chicone
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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