On the relationship between difference and projection-difference methods
Optimal order of convergence for stable evaluation of differential operators.
Orthogonal least squares solutions for linear operators.
Parallel methods in image recovery by projections onto convex sets
Periodic solutions to abstract differential equations
Pointwise Rational Approximation and Iterative Methods for Ill-Posed Problems.
Quand est-ce que des bornes de Hardy permettent de calculer une constante de Poincaré exacte sur la droite ?
Classically, Hardy’s inequality enables to estimate the spectral gap of a one-dimensional diffusion up to a factor belonging to . The goal of this paper is to better understand the latter factor, at least in a symmetric setting. In particular, we will give an asymptotical criterion implying that its value is exactly 4. The underlying argument is based on a semi-explicit functional for the spectral gap, which is monotone in some rearrangement of the data. To find it will resort to some regularity...
Quasi-iteration methods of Chebyshev type for the approximate solution of operator equations
Regularity problem for extremal vectors.
In this paper, we will use results developed by Ansari and Enflo in the theory of bounded linear operators with dense range. We define two maps, with regards to some parameters, that control surjectivity default of a given operator, and prove analycity for the first one and global continuity for the other one. Minimisation results are also obtained in relation to this study.
Remark on linear equations in Banach space
Remarks on quadratic equations in Banach space.
Remarques sur l'hypercontractivité et l'évolution de l'entropie pour des chaînes de Markov finies
Second order Cauchy problem with a damping operator.
Sequential regularization of ill-posed problems involving unbounded operators
Slowly decreasing entire functions and convolution equations
Small functions and iterative methods
Iterative methods based on small functions are used both to show local surjectivity of certain operators and a fixed point property of mappings on scales of complete metric spaces.
Solution operators for convolution equations on the germs of analytic functions on compact convex sets in
is compact and convex it is known for a long time that the nonzero constant coefficients linear partial differential operators (of finite or infinite order) are surjective on the space of all analytic functions on G. We consider the question whether solutions of the inhomogeneous equation can be given in terms of a continuous linear operator. For instance we characterize those sets G for which this is always the case.
Solvability of the functional equation f = (T-I)h for vector-valued functions
Let X be a reflexive Banach space and (Ω,,μ) be a probability measure space. Let T: M(μ;X) → M(μ;X) be a linear operator, where M(μ;X) is the space of all X-valued strongly measurable functions on (Ω,,μ). We assume that T is continuous in the sense that if (fₙ) is a sequence in M(μ;X) and in measure for some f ∈ M(μ;X), then also in measure. Then we consider the functional equation f = (T-I)h, where f ∈ M(μ;X) is given. We obtain several conditions for the existence of h ∈ M(μ;X) satisfying...
Some applications of the coincidence degree for set-contractions to functional differential equations of neutral type
Some insights into the regularization of ill-posed problems.