On applicability of the projection method to two-dimensional Toeplitz operators with measurable symbol.
The Weyl correspondence as a functional calculus
The aim of this paper is to use an abstract realization of the Weyl correspondence to define functions of pseudo-differential operators. We consider operators that form a self-adjoint Banach algebra. We construct on this algebra a functional calculus with respect to functions which are defined on the Euclidean space and have a finite number of derivatives.