Pseudodifferential Analysis on Conformally Compact Spaces

Buch | Softcover

2003
American Mathematical Society (Verlag)
978-0-8218-3272-1 (ISBN)

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The $0$-calculus on a manifold with boundary is a micro-localization of the Lie algebra of vector fields that vanish at the boundary. It has been used by Mazzeo, Melrose to study the Laplacian of a conformally compact metric. We give a complete characterization of those $0$-pseudodifferential operators that are Fredholm between appropriate weighted Sobolev spaces, and describe $C^{*}$-algebras that are generated by $0$-pseudodifferential operators. An important step is understanding the so-called reduced normal operator, or, almost equivalently, the infinite dimensional irreducible representations of $0$-pseudodifferential operators. Since the $0$-calculus itself is not closed under holomorphic functional calculus, we construct submultiplicative Frechet $*$-algebras that contain and share many properties with the $0$-calculus, and are stable under holomorphic functional calculus ($/Psi^{*}$-algebras in the sense of Gramsch). There are relations to elliptic boundary value problems.

Part 1. Fredholm theory for $0$-pseudodifferential operators: Review of basic objects of $0$-geometry The small $0$-calculus and the $0$-calculus with bounds The $b$-$c$-calculus on an interval The reduced normal operator Weighted $0$-Sobolev spaces Fredholm theory for $0$-pseudodifferential operators Part 2. Algebras of $0$-pseudodifferential operators of order $0$: $C^*$-algebras of $0$-pseudodifferential operators $/Psi^*$-algebras of $0$-pseudodifferential operators Appendix A. Spaces of conormal functions Bibliography Notations Index.

Erscheint lt. Verlag	1.5.2003
Reihe/Serie	Memoirs of the American Mathematical Society
Zusatzinfo	bibliography
Verlagsort	Providence
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	0-8218-3272-7 / 0821832727
ISBN-13	978-0-8218-3272-1 / 9780821832721
Zustand	Neuware