Factorization of matrix-functions and regularization of singular integral operators on manifolds with boundary.
Fefferman's SAK principle in one dimension
In this article we give a complete proof in one dimension of an a priori inequality involving pseudo-differential operators: if and are symbols in such that , then for all we have the estimate for all in the Schwartz space, where is the usual norm. We use microlocalization of levels I, II and III in the spirit of Fefferman’s SAK principle.
Feller semigroups, Dirchlet forms, and pseudo differential operators.
Feller semigroups obtained by variable order subordination.
Finite propagation speed and kernels of strictly elliptic operators.
Fonctions de mailles et théorie elliptique des opérateurs aux différences finies (suite)
Fonctions de mailles et théorie elliptique des opérateurs aux différences finies
Formes normales pour des opérateurs pseudodifférentiels semiclassiques en dimension 1
Formule de trace et applications
Formule de Weyl pour une classe d’opérateurs pseudodifférentiels d’ordre négatif sur
Fredholmness of pseudo-differential operators with nonregular symbols
We establish the Fredholmness of a pseudo-differential operator whose symbol is of class , , in the spatial variable. Our work here refines the work of H. Abels, C. Pfeuffer (2020).
From pseudodifferential analysis to modular form theory
Taking advantage of methods originating with quantization theory, we try to get some better hold - if not an actual construction - of Maass (non-holomorphic) cusp-forms. We work backwards, from the rather simple results to the mostly devious road used to prove them.
Front d'onde analytique et décomposition microlocale des distributions
On étudie en détail une décomposition microlocale analytique de la distribution 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...
Functional calculi for pseudodifferential operators, III
Fundamental solutions of pseudo-differential operators over -adic fields
Further pseudodifferential operators generating Feller semigroups and Dirichlet forms.
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
We discuss a recent necessary and sufficient condition for Melin's inequality for a class of systems of pseudodifferential operators.
Gevrey hypoellipticity for partial differential equations with characteristics of higher multiplicity.
Hyperbolic Cauchy problem and Leray's residue formula
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.
Hyperbolic equations with non-Lipschitz coefficients.