New Results on the DLp-Type Spaces Associated with a Singular Second Order Differential Operator

2015 ◽  
Vol 7 (3) ◽  
pp. 37-56
Author(s):  
Mourad Jelassi
Keyword(s):  
Differential Operator ◽  
Second Order ◽  
Order Differential Operator ◽  
Type Spaces

scholarly journals Sobolev-Type Spaces on the Dual of the Chébli-Trimèche Hypergroup and Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Mourad Jelassi ◽  
Hatem Mejjaoli
Keyword(s):  
Differential Operator ◽  
Type Theorem ◽  
Reproducing Kernels ◽  
Second Order ◽  
Order Differential Operator ◽  
Sobolev Type ◽  
Weierstrass Transform ◽  
Sobolev Type Spaces ◽  
Type Spaces

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.

Fractional Sobolev type spaces associated with a singular differential operator and applications

2014 ◽  
Vol 17 (2) ◽  
Author(s):  
Mourad Jelassi ◽  
Hatem Mejjaoli
Keyword(s):  
Wave Equation ◽  
Differential Operator ◽  
Second Order ◽  
Order Differential Operator ◽  
Sobolev Type ◽  
Fractional Operator ◽  
Singular Differential Operator ◽  
Sobolev Type Spaces ◽  
Type Spaces ◽  
Generalized Wave Equation

AbstractIn 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.

Stability of Solutions of Differential-operator and Operator-difference Equations in the Sense of Perturbation of Operators

2006 ◽  
Vol 6 (3) ◽  
pp. 269-290 ◽  
Author(s):  
B. S. Jovanović ◽  
S. V. Lemeshevsky ◽  
P. P. Matus ◽  
P. N. Vabishchevich
Keyword(s):  
Differential Operator ◽  
Difference Equations ◽  
Hyperbolic Equations ◽  
Second Order ◽  
Difference Schemes ◽  
Order Differential Operator ◽  
Stability Of Solutions ◽  
Operator Equations ◽  
The Difference ◽  
Coefficient Stability

Abstract Estimates of stability in the sense perturbation of the operator for solving first- and second-order differential-operator equations have been obtained. For two- and three-level operator-difference schemes with weights similar estimates hold. Using the results obtained, we construct estimates of the coefficient stability for onedimensional parabolic and hyperbolic equations as well as for the difference schemes approximating the corresponding differential problems.

The Expansion Theorems for Sturm-Liouville Operators with an Involution Perturbation

2021 ◽  
Author(s):  
Abdizhahan Sarsenbi
Keyword(s):  
Differential Operator ◽  
Differential Operators ◽  
Second Order ◽  
Order Differential Operator ◽  
Spectral Expansions ◽  
Sturm Liouville ◽  
Complex Valued ◽  
Liouville Operators

In this work, we studied the Green’s functions of the second order differential operators with involution. Uniform equiconvergence of spectral expansions related to the second-order differential operators with involution is obtained. Basicity of eigenfunctions of the second-order differential operator operator with complex-valued coefficient is established.

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