In this paper q-Sobolev type spaces are defined on R q by using the q-cosine Fourier transform and its inverse. In particular, embedding results for these spaces are established. Next we define the q-cosine potential and study some of its properties.

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In this paper, using the q2-Laplace transform early introduced by Abdi,1 we study q-wave Bessel polynomials related with the q-Bessel operator Δq,α. We show in particular that they are linked to the q-little Jacobi polynomials pn(x;α, β|q2).

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