On a class of unsolvable operators
On a proof of the boundedness and nuclearity of pseudodifferential operators in
On a symbol class of elliptic pseudodifferential operators
On Continuity of Singular Integral Operators in Sobolev Spaces.
On Function Spaces of Variable Order of Differentiation.
On Multi-Dimensional Random Walk Models Approximating Symmetric Space-Fractional Diffusion Processes
Mathematics Subject Classification: 26A33, 47B06, 47G30, 60G50, 60G52, 60G60.In this paper the multi-dimensional analog of the Gillis-Weiss random walk model is studied. The convergence of this random walk to a fractional diffusion process governed by a symmetric operator defined as a hypersingular integral or the inverse of the Riesz potential in the sense of distributions is proved.* Supported by German Academic Exchange Service (DAAD).
On multilinear singular integrals of Calderón-Zygmund type.
A variety of results regarding multilinear singular Calderón-Zygmund integral operators is systematically presented. Several tools and techniques for the study of such operators are discussed. These include new multilinear endpoint weak type estimates, multilinear interpolation, appropriate discrete decompositions, a multilinear version of Schur's test, and a multilinear version of the T1 Theorem suitable for the study of multilinear pseudodifferential and translation invariant operators. A maximal...
On realizations related to Weyl operators.
On some analytical index formulas related to operator-valued symbols.
On spectra of geometric operators on open manifolds and differentiable groupoids.
On the asymptotic convergence of the polynomial collocation method for singular integral equations and periodic pseudodifferential equations
We prove the convergence of polynomial collocation method for periodic singular integral, pseudodifferential and the systems of pseudodifferential equations in Sobolev spaces via the equivalence between the collocation and modified Galerkin methods. The boundness of the Lagrange interpolation operator in this spaces when allows to obtain the optimal error estimate for the approximate solution i.e. it has the same rate as the best approximation of the exact solution by the polynomials.
On the Fefferman-Phong inequality
We show that the number of derivatives of a non negative 2-order symbol needed to establish the classical Fefferman-Phong inequality is bounded by improving thus the bound obtained recently by N. Lerner and Y. Morimoto. In the case of symbols of type , we show that this number is bounded by ; more precisely, for a non negative symbol , the Fefferman-Phong inequality holds if are bounded for, roughly, . To obtain such results and others, we first prove an abstract result which says that...
On the identity of minimal and maximal realizations related to Fourier series operators
On the inversion of pseudo-differential operators
On the -adic spectral analysis and multiwavelet on .
On the solvability of pseudodifferential operators
On trace theorems for pseudo-differential operators
Opérateurs intégraux de Fourier et calcul de Weyl-Hörmander (cas d'une métrique symplectique)
Opérateurs pseudo-différentiels analytiques et opérateurs d'ordre infini
Cet article reprend et complète la partie qui concerne les opérateurs pseudo- différentiels analytiques dans un travail fait en collaboration avec P. Krée (Ann. Inst. Fourier, 17-1 (1967), 295-323). En particulier la théorie est généralisée aux opérateurs d’ordre infini.
Opérateurs pseudo-différentiels définis en un point
We introduce the notion of pseudo-differential operators defined at a point and we establish a canonical one-to-one correspondence between such an operator and its symbol. We also prove the invertibility theorem for special type operators.