Abstract

In this course we intend to give a brief introduction to pseudodifferential operators. Pseudodifferential operators have become one of the most important tools in the modern study of differential equations, allowing one to study variable coefficient operators and singularities of distributions. After introducing pseudodifferential operators and the calculus of their symbols, we shall turn to the construction of a type of inverse operator, a parametrix, which will be a solution operator to a differential equation. We will explore under what conditions a parametrix exists, and what can be said about the regularity of the solution. We will finish with a application to boundary value problems. The background required of this course is a familiarity with real and complex analysis, and some functional analysis. The lectures should be accessible to a first or second year graduate student of mathematics.

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