On the $q$-Bessel Fourier transform

Lazhar Dhaouadi (1)

1 Analyse harmonique et fonctions spéciales

In this work, we are interested by the $q$-Bessel Fourier transform with a new approach. Many important results of this $q$-integral transform are proved with a new constructive demonstrations and we establish in particular the associated $q$-Fourier-Neumen expansion which involves the $q$-little Jacobi polynomials.

Domaines: Analyse classique [math.CA]

Lazhar Dhaouadi. On the $q$-Bessel Fourier transform. Bulletin of Mathematical Analysis and Applications, 2013, 5 (2), pp.42-60. ⟨hal-00322168v4⟩