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Hardy-type theorem for orthogonal functions with respect to their zeros. The Ja...
Abreu, L. D.; Marcellan, F.; Yakubovich, S. B.Motivated by the G.H. Hardy's 1939 results [G.H. Hardy, Notes on special systems of orthogonal functions II: On functions orthogonal with respect to their own zeros, J. London Math. Soc. 14 (1939) 37-44] on functions orthogonal with respect to their real zeros [lambda]n, , we will consider, under the same general conditions imposed by Hardy, functions satisfying an orthogonality with respect to their zeros with...
Pointwise convergent expansions in q-Fourier-Bessel series
Abreu, L. D.; Alvarez-Nodarse, R.; Cardoso, J. L.We define q-analogues of Fourier-Bessel series, by means of complete q- orthogonal systems constructed with the third Jackson q-Bessel function. Sufficient conditions for pointwise convergence of these series are obtained, in terms of a general convergence principle valid for other Fourier series on grids defined over numerable sets. The results are illustrated with specific examples of developments in q-Fourie...
Completeness criteria for sequences of special functions
Abreu, L. D.Two Lp completeness criteria for sequences of functions written in the form f(lnx), where ln is the nth zero of another function g, are obtained. The results are illustrated with applications to sequences of special functions ; Fundação para a Ciência e Tecnologia; Centro de Matemática da Universidade de Coimbra
A q-sampling theorem related to the q-Hankel transform
Abreu, L. D.A q-version of the sampling theorem is derived using the q-Hankel transform introduced by Koornwinder and Swarttouw. The sampling points are the zeros of the third Jackson q-Bessel function ; Fundação para a Ciência e Tecnologia; Centro de Matemática da Universidade de Coimbra
The roots of the third Jackson q-Bessel function
Abreu, L. D.; Bustoz, J.; Cardoso, J. L.We derive analytic bounds on the roots of the third Jackson Function. This bounds prove a conjecture of M. E. H. Ismail concerning the asymptotic behaviour of the roots.
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