We consider a perturbed system of exponents { en } n∈Z, when the sequence {λn }n∈Z has a definite asymptotics. We study basis properties (completeness, minimality, basicity) of this system in Lebesgue space of functions Lp(·) (−π, π) with variable summability exponent p(·), subject to parameters contained in the asymptotics {λn}n∈Z.

The present paper deals with a Kirchhoff problem under homogeneous Dirichlet boundary conditions, set in a bounded smooth domain Ω of R^{N}. The problem studied is a stationary version of the orig inal Kirchhoff equation, involving the p(x)-Lap lacian operator, in the framework of the variable exponent Lebesgue and Sobolev spaces. The question of the existence of weak solutions is treated. Appl...

In this work, approximation properties of de la Vall?e-Poussin means are investigated in weighted Lebesgue spaces with variable exponent where weight function belongs to Muckenhoupt class. For purpose direct, inverse and simultaneous theorems theory proved constructive characterizations functions obtained exponent.

A hybrid inversion scheme for through-the-wall imaging is proposed in this paper. The approach based on a linearized model of the inverse-scattering problem, employing Green’s function developed layered background. reconstruction obtained by means Landweber-like iterative method performing regularization framework variable-exponent Lebesgue spaces. Thanks to non-conventional geometrical propert...

We consider structured optimisation problems defined in terms of the sum a smooth and convex function, proper, l.s.c., (typically non-smooth) one reflexive variable exponent Lebesgue spaces $L_{p(\cdot)}(\Omega)$. Due to their intrinsic space-variant properties, such can be naturally used as solution space combined with functionals for ill-posed inverse problems. For this purpose, we propose an...