(About Jackson q-Bessel functions) Laplace transform allows to resolve differential equations in the neighborhood of an irregular singular point. The purpose of the article is to study how to apply a basic Borel– Laplace transformation to q-difference equations satisfied by the q-Bessel functions of F.H. Jackson. Connection matrices are obtained between solutions at the origin and solutions at ...

We construct the Plancherel measure corresponding to the Bessel model on the split special orthogonal group of odd degree ≥ 5 and the Whittaker model on a connected split reductive group in general. As an application we prove the inversion formula which expresses the related integral transform in terms of the Satake transform.

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.

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.