On a pseudodifferential calculus with modest boundary decay condition

<p>A boundary decay condition, called vanishing to infinite logarithmic order is introduced. A pseudodifferential calculus, extending the <em> b</em>-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.</p>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematical Sciences

Year

2018

Author dc:creator

• Huang, Binbin

Contributors dc:contributor

• Paul A. Loya

• Pure sciences
• B-calculus
• Dirac operator
• Heat kernel
• Index theory
• Pseudodifferential operator
• Mathematics

Repository record dc:identifier

https://orb.binghamton.edu/dissertation_and_theses/36

OAI identifier oai:identifier

oai:orb.binghamton.edu:dissertation_and_theses-1051