Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 1978 / Vita. / Bibliography: leaves 96-97. / Ph. D. / Ph. D. Massachusetts Institute of Technology, Department of Mathematics

A Thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg for the Degree of Doctor of Philosophy. Johannesburg, 1979

Thesis (Ph.D.)--University of Missouri-Columbia, 2006. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (February 27, 2007) Vita. Includes bibliographical references.

We introduce a natural symmetry condition for a pseudodifferential operator on a manifold with cylindrical ends ensuring that the operator admits a doubling across the boundary. For such operators we prove an explicit index formula containing, apart from the Atiyah-Singer integral, a finite number of residues of the logarithmic derivative of the conormal symbol.

We construct a class of elliptic operators in the edge algebra on a manifold M with an embedded submanifold Y interpreted as an edge. The ellipticity refers to a principal symbolic structure consisting of the standard interior symbol and an operator-valued edge symbol. Given a differential operator A on M for every (sufficiently large) s we construct an associated operator As in the edge calculus. We show that ellipticity of A in the usual sense entails ellipticity of As as an edge operator (up to a discrete set of reals s). Parametrices P of A then correspond to parametrices Ps of As, interpreted as Mellin-edge representations of P.

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 162-169). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 162-169). Also available on the Internet.

Thesis (Ph.D.)--Mathematics, Georgia Institute of Technology, 2008. / Committee Chair: Dieci, Luca; Committee Member: Chow, Shui-Nee; Committee Member: Liu, Yingjie; Committee Member: Loss, Michael; Committee Member: Verriest, Erik.

Originally presented as the author's thesis, Bonn. / Added t.p. with thesis statement inserted. Bibliography: p. 78-80.

Thesis (doctoral)--Rheinische-Friedrich-Wilhelms-Universität. / Title has symbol for mean partial differential operator. Includes bibliographical references.