Mourad Jelassi - Academia.edu (original) (raw)
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Papers by Mourad Jelassi
International Journal of Open Problems in Complex Analysis, 2015
In this work, we consider a second order differential operator A defined on (0, +∞), where A is a... more In this work, we consider a second order differential operator A defined on (0, +∞), where A is a non negative function satisfying some conditions. To A we associate D Lp-type spaces denoted by D p A. Some results, related to the spaces D p A , are proved. Moreover A generalization of Titchmarsh's theorem for the Chébli-Trimèche transfrom in D 2 A is established.
Fractional Calculus and Applied Analysis, 2014
In this paper we introduce and we study fractional Sobolev type spaces associated with a singular... more In this paper we introduce and we study fractional Sobolev type spaces associated with a singular second order differential operator on (0, ∞) and propose several results. As applications we give certain properties including estimates for the solution of the generalized wave equation and generalized fractional operator.
Abstract and Applied Analysis, 2014
We define and study Sobolev-type spacesWAs,pℝ+associated with singular second-order differential ... more We define and study Sobolev-type spacesWAs,pℝ+associated with singular second-order differential operator on0,∞. Some properties are given; in particular we establish a compactness-type imbedding result which allows a Reillich-type theorem. Next, we introduce a generalized Weierstrass transform and, using the theory of reproducing kernels, some applications are given.
Operators and Matrices, 2015
In this paper we consider multivariable Bessel operator. We define and study the multivariable Be... more In this paper we consider multivariable Bessel operator. We define and study the multivariable Bessel Gabor transform. We prove a Plancherel formula, an inversion formula and a weak uncertainty principle for it. As applications, an analog of Heisenberg's inequality is obtained. At the end, we give an application of the theory of reproducing kernels to the Tikhonov regularization on the generalized Sobolev spaces associated with the multivariable Bessel operator.
International Journal of Open Problems in Complex Analysis, 2015
In this work, we consider a second order differential operator A defined on (0, +∞), where A is a... more In this work, we consider a second order differential operator A defined on (0, +∞), where A is a non negative function satisfying some conditions. To A we associate D Lp-type spaces denoted by D p A. Some results, related to the spaces D p A , are proved. Moreover A generalization of Titchmarsh's theorem for the Chébli-Trimèche transfrom in D 2 A is established.
Fractional Calculus and Applied Analysis, 2014
In this paper we introduce and we study fractional Sobolev type spaces associated with a singular... more In this paper we introduce and we study fractional Sobolev type spaces associated with a singular second order differential operator on (0, ∞) and propose several results. As applications we give certain properties including estimates for the solution of the generalized wave equation and generalized fractional operator.
Abstract and Applied Analysis, 2014
We define and study Sobolev-type spacesWAs,pℝ+associated with singular second-order differential ... more We define and study Sobolev-type spacesWAs,pℝ+associated with singular second-order differential operator on0,∞. Some properties are given; in particular we establish a compactness-type imbedding result which allows a Reillich-type theorem. Next, we introduce a generalized Weierstrass transform and, using the theory of reproducing kernels, some applications are given.
Operators and Matrices, 2015
In this paper we consider multivariable Bessel operator. We define and study the multivariable Be... more In this paper we consider multivariable Bessel operator. We define and study the multivariable Bessel Gabor transform. We prove a Plancherel formula, an inversion formula and a weak uncertainty principle for it. As applications, an analog of Heisenberg's inequality is obtained. At the end, we give an application of the theory of reproducing kernels to the Tikhonov regularization on the generalized Sobolev spaces associated with the multivariable Bessel operator.