On Pseudo-Differential Operators and Smoothness of Special Lie-Group Representations.
On realizations related to Weyl operators.
On some analytical index formulas related to operator-valued symbols.
On the Dirichlet and Neumann problems in multi-dimensional cone
We consider an elliptic pseudodifferential equation in a multi-dimensional cone, and using the wave factorization concept for an elliptic symbol we describe a general solution of such equation in Sobolev-Slobodetskii spaces. This general solution depends on some arbitrary functions, their quantity being determined by an index of the wave factorization. For identifying these arbitrary functions one needs some additional conditions, for example, boundary conditions. Simple boundary value problems,...
On the Eigenvalue problem of T'Hooft.
On the eigenvalues of a class of hypo-elliptic operators. IV
Let be a selfadjoint classical pseudo-differential operator of order with non-negative principal symbol on a compact manifold. We assume that is hypoelliptic with loss of one derivative and semibounded from below. Then exp, , is constructed as a non-classical Fourier integral operator and the main contribution to the asymptotic distribution of eigenvalues of is computed. This paper is a continuation of a series of joint works with A. Menikoff.
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 functoriality of stratified desingularizations.
On the hypoellipticity of pseudo-differential systems with a diagonal principal symbol
On the inversion of pseudo-differential operators
On the Laguerre calculus of left-invariant convolution (pseudo-differential) operators on the Heisenberg group
On the order of pointwise convergence of some boundary element methods. Part I. Operators of negative and zero order
On the Range of the Fourier Transform Associated with the Spherical Mean Operator
We characterize the range of some spaces of functions by the Fourier transform associated with the spherical mean operator R and we give a new description of the Schwartz spaces. Next, we prove a Paley-Wiener and a Paley-Wiener-Schawrtz theorems.
On the range of the Fourier transform connected with Riemann-Liouville operator
We characterize the range of some spaces of functions by the Fourier transform associated with the Riemann-Liouville operator and we give a new description of the Schwartz spaces. Next, we prove a Paley-Wiener and a Paley-Wiener-Schwartz theorems.
On the semi-classical approximation of the solution of the Heisenberg equation with spin
On the singularities of solutions of partial differential equations with constant coefficients
On the singularities of the solution of the Cauchy problem for the operator with non uniform multiple characteristics
On the solvability of a nonlocal problem arising in dynamics of moisture transfer.
On the solvability of pseudodifferential operators
On the spectral theory of pseudo-differential elliptic boundary problems