Lazhar Dhaouadi

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The prolate spheroidal wave functions, which are a special case of the spheroidal wave functions, possess a very surprising and unique property [6]. They are an orthogonal basis of both L2(−1, 1) and the Paley-Wiener space of bandlimited functions. They also satisfy a discrete orthogonality relation. No other system of classical orthogonal functions is(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.
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