Pseudo-differential Operators on ℝⁿ

Abstract

The subject of pseudo-differential operators on ℝⁿ is well studied and there are many excellent monographs on the subject, see, e.g., [27, 33, 55, 71, 101, 112, 130, 135, 152], as well as on the more general subject of Fourier integral operators, microlocal analysis, and related topics in, e.g., [30, 56, 45, 81, 113]. Therefore, here we only sketch main elements of the theory. In this chapter, we use the notation 〈ξ〉 = (1 + |ξ|²)^1/2.