Document Type
Dissertation
Date of Award
2018
Keywords
Pure sciences, B-calculus, Dirac operator, Heat kernel, Index theory, Pseudodifferential operator
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematical Sciences
First Advisor
Paul A. Loya
Subject Heading(s)
Pure sciences; B-calculus; Dirac operator; Heat kernel; Index theory; Pseudodifferential operator; Mathematics
Abstract
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.
Recommended Citation
Huang, Binbin, "On a pseudodifferential calculus with modest boundary decay condition" (2018). Graduate Dissertations and Theses. 36.
https://orb.binghamton.edu/dissertation_and_theses/36