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In this paper we introduce the q−Bessel Fourier transform, the q−Bessel translation operator and the q−convolution product. We prove that the q−heat semigroup is contractive and we establish the q−analogue of Babenko inequalities associated to the q−Bessel Fourier transform. With applications and finally we enunciate a q−Bessel version of the central limit(More)
Spectral theory from the second-order q-difference operator Δ q is developed. We give an integral representation of its inverse, and the resolvent operator is obtained. As application , we give an analogue of the Poincare inequality. We introduce the Zeta function for the operator Δ q and we formulate some of its properties. In the end, we obtain the(More)
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.