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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)

- Lazhar Dhaouadi
- 2008

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 L 2 (−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)

- Lazhar Dhaouadi
- 2008

It is the purpose of this note to give a new interpretation of the Graf's addition formula for Hahn Exton q-Bessel function using the properties of the q-Bessel Fourier transform. In the rest of this note we establish a connection between this result and the positivity of the q-Bessel translation operator.

- Lazhar Dhaouadi
- 2008

In this paper we give a q-analogue of the Hardy's theorem for the q-Bessel Fourier transform. The celebrated theorem asserts that if a function f and its Fourier transform f satisfying |f (x)| ≤ c.e

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)

- Lazhar Dhaouadi
- 2013

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.

- Lazhar Dhaouadi
- 2008

In this paper we uses an I.I. Hirschman-W. Beckner entropy argument to give an uncertainty inequality for the q-Bessel Fourier transform: F q,v f (x) = c q,v ∞ 0 f (t)j v (xt, q 2)t 2v+1 d q t, where j v (x, q) is the normalized Hahn-Exton q-Bessel function.

- Lazhar Dhaouadi, Edward Charles Titchmarsh
- 2008

The aim of this paper is to study the q-Schrödinger operator L = q(x) − ∆ q , where q(x) is a given function of x defined over R + q = {q n , n ∈ Z} and ∆ q is the q-Laplace operator ∆ q f (x) = 1 x 2 f (q −1 x) − 1 + q q f (x) + 1 q f (qx) .

- Lazhar Dhaouadi
- 2008

In this paper there are many important results of q-Fourier analysis proved by new ways and new sets of markov operators acting on the L q,2,v space of square q-integrable function which were defined.