Entire vectors and time reversible Cauchy problems.
Entropy and approximation numbers of embeddings between weighted Besov spaces
The present paper is devoted to the study of the “quality” of the compactness of the trace operator. More precisely, we characterize the asymptotic behaviour of entropy numbers of the compact map , where Γ is a d-set with 0 < d < n and a weight of type near Γ with ϰ > -(n-d). There are parallel results for approximation numbers.
Entropy and approximation numbers of embeddings of function spaces with Muckenhoupt weights, I.
Entropy and Eigenvalues of Certain Integral Operators.
Entropy and n-widths of operators in Banach spaces
Entropy considerations in the noncommutative setting.
Entropy numbers of certain summation operators.
Entropy numbers of diagonal operators of logarithmic type.
Entropy numbers of embeddings between logarithmic Sobolev spaces.
Entropy numbers of general diagonal operators.
We determine the asymptotic behavior of the entropy numbers of diagonal operators D: lp → lq, (xk) → (skxk), 0 < p,q ≤ ∞, under mild regularity and decay conditions on the generating sequence (σk). Our results extend the known estimates for polynomial and logarithmic diagonals (σk). Moreover, we also consider some exotic intermediate examples like (σk)=exp(-√log k).
Entropy numbers of r-nuclear operators between spaces
Entropy numbers of r-nuclear operators in Banach spaces of type q
Entropy of a doubly stochastic Markov operator and of its shift on the space of trajectories
We define the space of trajectories of a doubly stochastic operator on L¹(X,μ) as a shift space , where ν is a probability measure defined as in the Ionescu-Tulcea theorem and σ is the shift transformation. We study connections between the entropy of a doubly stochastic operator and the entropy of the shift on the space of trajectories of this operator.
Entropy of -valued operators and diverse applications.
Epi/hypo-convergence: The slice topology and saddle points approximation.
Equality of coarse topologies in inverse transformations
Équation d’évolution sur , avec condition en plusieurs points
Equation with residuated functions
The structure of solution-sets for the equation is discussed, where are given residuated functions mapping between partially-ordered sets. An algorithm is proposed which produces a solution in the event of finite termination: this solution is maximal relative to initial trial values of . Properties are defined which are sufficient for finite termination. The particular case of max-based linear algebra is discussed, with application to the synchronisation problem for discrete-event systems;...
Equations containing locally Henstock-Kurzweil integrable functions
A fixed point theorem in ordered spaces and a recently proved monotone convergence theorem are applied to derive existence and comparison results for solutions of a functional integral equation of Volterra type and a functional impulsive Cauchy problem in an ordered Banach space. A novel feature is that equations contain locally Henstock-Kurzweil integrable functions.
Equations de Fokker-Planck géométriques II : estimations hypoelliptiques maximales
Nous donnons des résultats analytiques sur les propriétés de régularité du laplacien hypoelliptique de Jean-Michel Bismut et plus généralement sur les opérateurs de type Fokker-Planck géométrique agissant sur le fibré cotangent d’une variété riemannienne compacte . En particulier, nous prouvons un résultat d’hypoellipticité maximale pour , et nous en déduisons des bornes sur la localisation de ses valeurs spectrales.