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- 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 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)

- 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: Fq,vf(x) = cq,v ∫ ∞ 0 f(t)jv(xt, q 2)t2v+1dqt, where jv(x, q) is the normalized Hahn-Exton q-Bessel function.

- Lazhar Dhaouadi
- Int. J. Math. Mathematical Sciences
- 2007

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, 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 = {qn, n ∈ Z} and ∆q is the q-Laplace operator ∆qf(x) = 1 x [ f(qx)− 1 + q q f(x) + 1 q f(qx) ]

- Lazhar Dhaouadi
- Applied Mathematics and Computation
- 2013

- 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

Sufficient condition for the symmetric moment problem to be determinate is given using standards methods of q-Fourier analysis. This condition it cannot be a particular case of Carleman’s criterion.

- 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. 1 Preliminaries Throughout this paper we consider 0… (More)

- 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 Lq,2,v space of square q-integrable function which were defined.

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