In these lecture notes we introduce some of the concepts and results from microlocal analysis used in the analysis of boundary value problems for elliptic differential operators, with a special emphasis on Dirac-like operators. We first consider the problem of finding elliptic boundary conditions for the ∂̄operator on the unit disk. The rather explicit results in this special case delineate the ...

For a second-order symmetric strongly elliptic differential operator on an exterior domain in Rn it is known from works of Birman and Solomiak that a change of the boundary condition from the Dirichlet condition to an elliptic Neumann or Robin condition leaves the essential spectrum unchanged, in such a way that the spectrum of the difference between the inverses satisfies a Weyl-type asymptoti...

Abstract. Here a new condition for the geometry of Banach spaces is introduced and the operator–valued Fourier multiplier theorems in weighted Besov spaces are obtained. Particularly, connections between the geometry of Banach spaces and Hörmander-Mikhlin conditions are established. As an application of main results the regularity properties of degenerate elliptic differential operator equation...