Propriétés locales d'espaces de type Sobolev en dimension infinie
Protenseurs distributions
Pseudodifferential Operators
Pseudodifferential operators on non-quasianalytic classes of Beurling type
We introduce pseudodifferential operators (of infinite order) in the framework of non-quasianalytic classes of Beurling type. We prove that such an operator with (distributional) kernel in a given Beurling class is pseudo-local and can be locally decomposed, modulo a smoothing operator, as the composition of a pseudodifferential operator of finite order and an ultradifferential operator with constant coefficients in the sense of Komatsu, both operators with kernel in the same class . We also...
Pseudodifferential operators with generalized symbols and regularity theory.
Quantum Itô algebra and quantum martingale
In this paper, we study a representation of the quantum Itô algebra in Fock space and then by using a noncommutative Radon-Nikodym type theorem we study the density operators of output states as quantum martingales, where the output states are absolutely continuous with respect to an input (vacuum) state. Then by applying quantum martingale representation we prove that the density operators of regular, absolutely continuous output states belong to the commutant of the ⋆-algebra parameterizing the...
Quantum Lévy-type Laplacian and associated stochastic differential equations
We study a quantum extension of the Lévy Laplacian, so-called quantum Lévy-type Laplacian, to the nuclear algebra of operators on spaces of entire functions. We give several examples of the action of the quantum Lévy-type Laplacian on basic operators and we study a quantum white noise convolution differential equation involving the quantum Lévy-type Laplacian.
Quasiasymptotic expansion of distributions from and the asymptotic expansion of the distributional Stieltjes transform.
Quasiasymptotic expansion of distributions with applications to the Stieltjes transform
Quasi-discrete dynamics of a neural net: The lighthouse model.
Quasi-isometric vector bundles and bounded factorization of holomorphic matrices
We give a sufficient condition for a hermitian holomorphic vector bundle over the disk to be quasi-isometric to the trivial bundle. One consequence is a version of Cartan's lemma on the factorization of matrices with uniform bounds.
Quelques applications des éspaces de Silva et de leurs duals
Quelques propriétés du noyau d'un opérateur différentiel linéaire non hypoelliptique, à coefficients constants
Quelques Proprietes sur le Produit Tensoriel des Distributions Stochastiques du Schwartz
Quelques théorèmes de décomposition des ultradistributions
Deux décompositions d’une fonctionnelle d’un espace d’ultra-distributions sont étudiées. La première fait intervenir une série convergente de dérivées de mesures dont on montre que les supports peuvent être pris inclus dans le support . La seconde consiste à exprimer comme somme de fonctionnelles du même espace portées par les éléments d’une partition du support de . Dans les deux cas on a recours à des concepts de régularité et de séparation régulière d’ensembles fermés de qui relient la...
Randverteilungen holomorpher Funktionen und die Topologie von D'.
Range of operators and regularity of solutions
Range of the horocyclic Radon transform on trees
In this paper we study the Radon transform on the set of horocycles of a homogeneous tree , and describe its image on various function spaces. We show that the functions of compact support on that satisfy two explicit Radon conditions constitute the image under of functions of finite support on . We extend these results to spaces of functions with suitable decay on , whose image under satisfies corresponding decay conditions and contains distributions on that are not defined pointwise....
Real and complex fundamental solutions. A way for unifying mathematical analysis.
Recent development in the theory of linear partial differential equations.