Pseudodifferential Analysis on Conformally Compact Spaces.

Intro -- Contents -- Introduction -- Acknowledgments: -- Part 1. Predholm 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[sup(2)][sub(0)] -- 1.4. The extended 0-triple space X[sup(3)][sub(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[sub(+)]-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[sup(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 Ψ[sup(0)][sub(0)](X -- [sup(0)]Ω[sup(1/2)]).

6.3. Characterization of Fredholm operators inΨ[sup(m,k)][sub(0)](X -- [sup(0)]Ω[sup(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*∂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[sup((a))][sub(0)](X,[sup(0)]Ω[sup(1/2)]) -- 7.6. The spectrum of the C*-algebra B[sup((a))][sub(0)](X,[sup(0)]Ω[sup(1/2)]) -- Chapter 8. Ψ*-algebras of 0-pseudodifferential operators -- 8.1. Submultiplicative Ψ*-algebras -- 8.2. Ψ*-completions of b-c-and 0-calculus -- Appendix A. Spaces of conormal functions -- Bibliography -- Notations -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- L -- M -- N -- O -- P -- R -- S -- T -- V -- W.

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