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Front d'onde analytique et décomposition microlocale des distributions

Pascal Laubin (1983)

Annales de l'institut Fourier

On étudie en détail une décomposition microlocale analytique de la distribution δ ( x - y ) suivant des distributions singulières en un seul point et dans une seule codirection. Cette décomposition est obtenue à partir d’opérateurs Fourier-Intégraux à phases complexes.On utilise ensuite cet outil pour démontrer le théorème de décomposition du front d’onde analytique des distributions. On établit également des théorèmes concernant la représentation globale des distributions comme sommes de valeurs au bord...

Further pseudodifferential operators generating Feller semigroups and Dirichlet forms.

Niels Jacob (1993)

Revista Matemática Iberoamericana

We prove for a large class of symmetric pseudo differential operators that they generate a Feller semigroup and therefore a Dirichlet form. Our construction uses the Yoshida-Hille-Ray Theorem and a priori estimates in anisotropic Sobolev spaces. Using these a priori estimates it is possible to obtain further information about the stochastic process associated with the Dirichlet form under consideration.

Generalizations of Melin's inequality to systems

Raymond Brummelhuis (2001)

Journées équations aux dérivées partielles

We discuss a recent necessary and sufficient condition for Melin's inequality for a class of systems of pseudodifferential operators.

Global time estimates for solutions to equations of dissipative type

Michael Ruzhansky, James Smith (2005)

Journées Équations aux dérivées partielles

Global time estimates of L p - L q norms of solutions to general strictly hyperbolic partial differential equations are considered. The case of special interest in this paper are equations exhibiting the dissipative behaviour. Results are applied to discuss time decay estimates for Fokker-Planck equations and for wave type equations with negative mass.

Gradient flows of the entropy for jump processes

Matthias Erbar (2014)

Annales de l'I.H.P. Probabilités et statistiques

We introduce a new transport distance between probability measures on ℝ d that is built from a Lévy jump kernel. It is defined via a non-local variant of the Benamou–Brenier formula. We study geometric and topological properties of this distance, in particular we prove existence of geodesics. For translation invariant jump kernels we identify the semigroup generated by the associated non-local operator as the gradient flow of the relative entropy w.r.t. the new distance and show that the entropy is...

Hyperbolic Cauchy problem and Leray's residue formula

Susumu Tanabé (2000)

Annales Polonici Mathematici

We give an algebraic description of (wave) fronts that appear in strictly hyperbolic Cauchy problems. A concrete form of a defining function of the wave front issued from the initial algebraic variety is obtained with the aid of Gauss-Manin systems satisfied by Leray's residues.

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