Date of Award

Summer 7-16-2014

Document Type

Thesis

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

First Advisor

Markus Pflaum

Second Advisor

Florian Sobieczky

Third Advisor

Judith Packer

Abstract

Starting with the normal symbold of M. Pflaum, we generalize the machinery of global symbol calculi from the familiar setting of a compact Riemannian manifold to the b-calculus on a compact manifold-with-boundary, endowed with an exact b-metric. We define a notion of b-linearization, crucial to the symbol calculus. and show that an exact b-metric can be used to construct a b-linearization. Using the b-linearization, we define the global symbol of a b-pseudodifferential operator as a fiberwise Fourier transform over the b-tangent bundle. We prove that the global symbol is truly a symbol, of the same order of its operator, and define a quantization map with which one can recover the operator (modulo b-smoothing operators.) We compute the global symbol for a b-Laplacian, and give a formula for the b-trace in terms of the global symbol.

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Mathematics Commons

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