Date of Award
Doctor of Philosophy (PhD)
Paul A. Loya
A boundary decay condition, called vanishing to infinite logarithmic order is introduced. A pseudodifferential calculus, extending the b-calculus of Melrose, is proposed based on this modest decay condition. The mapping properties, composition rule, and normal operators are studied. Instead of functional analytic methods, a geometric approach is invoked in pursuing the Fredholm criterion. As an application, a detailed proof of the Atiyah-Patodi-Singer index theorem, including a review of Dirac operators of product type and construction of the heat kernel, is presented.
Huang, Binbin, "On a Pseudodifferential Calculus with Modest Boundary Decay Condition" (2018). Graduate Dissertations and Theses. 36.