Pseudodifferential analysis on conformally compact spaces /
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| Author / Creator: | Lauter, Robert, 1967- |
|---|---|
| Imprint: | Providence, RI : American Mathematical Society, 2003. |
| Description: | xvi, 92 p. ; 26 cm. |
| Language: | English |
| Series: | Memoirs of the American Mathematical Society, 0065-9266 ; no. 777 |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/4849118 |
Table of Contents:
- Introduction
- Acknowledgments
- Part 1.. Fredholm theory for 0-pseudodifferential operators
- Chapter 1.. Review on basic objects of 0-geometry
- 1.1.. The 0-structure algebra
- 1.2.. The extended 0-blow up
- 1.3.. Relation to the 0-double space X[superscript 2 subscript 0]
- 1.4.. The extended 0-triple space X[superscript 3 subscript 0,e]
- 1.5.. 0-densities
- Chapter 2.. The small 0-calculus and the 0-calculus with bounds
- 2.1.. The Schwartz kernel theorem revisited
- 2.2.. The small 0-calculus
- 2.3.. Basic properties of the small 0-calculus
- 2.4.. The 0-calculus with bounds
- 2.5.. Basic properties of the 0-calculus with bounds
- 2.6.. The indicial function
- 2.7.. General bundles
- Chapter 3.. The b-c-calculus on an interval
- 3.1.. The b-c-structure algebra
- 3.2.. The b-c-double space
- 3.3.. b-c-densities
- 3.4.. The b-c-calculus with bounds
- 3.5.. Basic properties of the b-c-calculus
- 3.6.. Fredholm theory for the b-c-calculus
- 3.7.. Invariance of the b-c-calculus under the R[subscript +]-action
- 3.8.. C*-algebras of b-c-operators
- 3.9.. General bundles
- Chapter 4.. The reduced normal operator
- 4.1.. Definition of the reduced normal operator
- 4.2.. Coordinate invariance of the reduced normal operator
- 4.3.. Scale invariance of the reduced normal operator
- 4.4.. Characterization of the reduced normal operator
- 4.5.. Basic properties of the reduced normal operator
- 4.6.. The case of 0-differential operators
- 4.7.. General bundles
- Chapter 5.. Weighted 0-Sobolev spaces
- 5.1.. Boundedness of 0-operators of order 0 on L[superscript 2]-spaces
- 5.2.. Weighted 0-Sobolev spaces
- 5.3.. General bundles
- Chapter 6.. Fredholm theory for 0-pseudodifferential operators
- 6.1.. Symbol reproducing families
- 6.2.. Characterization of Fredholm operators in [psi superscript 0 subscript 0](X; [superscript 0 Omega superscript 1/2])
- 6.3.. Characterization of Fredholm operators in [psi superscript m,k subscript 0](X; [superscript 0 Omega superscript 1/2])
- 6.4.. General bundles
- Part 2.. Algebras of 0-pseudodifferential operators of order 0
- Chapter 7.. C*-algebras of 0-pseudodifferential operators
- 7.1.. Solvable C*-algebras
- 7.2.. The reduced normal operator on S*[partial differential]X
- 7.3.. Extension of the symbolic structure
- 7.4.. The C*-algebra generated by the reduced normal operator
- 7.5.. The C*-algebra B[superscript (a) subscript 0](X, [superscript 0 Omega superscript 1/2])
- 7.6.. The spectrum of the C*-algebra B[superscript (a) subscript 0](X, [superscript 0 Omega superscript 1/2])
- Chapter 8.. [psi]*-algebras of 0-pseudodifferential operators
- 8.1.. Submultiplicative [psi]*-algebras
- 8.2.. [psi]*-completions of b-c- and 0-calculus
- Appendix A.. Spaces of conormal functions
- Bibliography
- Notations
- Index
