Pseudodifferential analysis on conformally compact spaces / Robert Lauter.

Format:

Book

Author/Creator:

Lauter, Robert, 1967-

Series:

Memoirs of the American Mathematical Society 0065-9266 ; no. 777.

Memoirs of the American Mathematical Society, 0065-9266 ; no. 777

Language:

English

Subjects (All):

Pseudodifferential operators.

Compact spaces.

Manifolds (Mathematics).

Physical Description:

xvi, 92 pages ; 26 cm.

Place of Publication:

Providence, RI : American Mathematical Society, 2003.

Contents:

Part 1. Fredholm theory for 0-pseudodifferential operators 1

Chapter 1. Review on basic objects of 0-geometry 3

1.1. The 0-structure algebra 3

1.2. The extended 0-blow up 4

1.3. Relation to the 0-double space X[superscript 2 subscript 0] 6

1.4. The extended 0-triple space X[superscript 3 subscript 0,e] 7

1.5. 0-densities 9

Chapter 2. The small 0-calculus and the 0-calculus with bounds 11

2.1. The Schwartz kernel theorem revisited 11

2.2. The small 0-calculus 11

2.3. Basic properties of the small 0-calculus 12

2.4. The 0-calculus with bounds 15

2.5. Basic properties of the 0-calculus with bounds 17

2.6. The indicial function 17

Chapter 3. The b-c-calculus on an interval 19

3.1. The b-c-structure algebra 19

3.2. The b-c-double space 19

3.3. b-c-densities 21

3.4. The b-c-calculus with bounds 21

3.5. Basic properties of the b-c-calculus 22

3.6. Fredholm theory for the b-c-calculus 24

3.7. Invariance of the b-c-calculus under the R[subscript +]-action 25

3.8. C*-algebras of b-c-operators 26

Chapter 4. The reduced normal operator 29

4.1. Definition of the reduced normal operator 29

4.2. Coordinate invariance of the reduced normal operator 30

4.3. Scale invariance of the reduced normal operator 31

4.4. Characterization of the reduced normal operator 32

4.5. Basic properties of the reduced normal operator 40

4.6. The case of 0-differential operators 42

Chapter 5. Weighted 0-Sobolev spaces 45

5.1. Boundedness of 0-operators of order 0 on L[superscript 2]-spaces 45

5.2. Weighted 0-Sobolev spaces 47

Chapter 6. Fredholm theory for 0-pseudodifferential operators 49

6.1. Symbol reproducing families 49

6.2. Characterization of Fredholm operators in [psi superscript 0 subscript 0](X; [superscript 0 Omega superscript 1/2]) 50

6.3. Characterization of Fredholm operators in [psi superscript m,k subscript 0](X; [superscript 0 Omega superscript 1/2]) 53

Part 2. Algebras of 0-pseudodifferential operators of order 0 55

Chapter 7. C*-algebras of 0-pseudodifferential operators 57

7.1. Solvable C*-algebras 57

7.2. The reduced normal operator on S*[partial differential]X 57

7.3. Extension of the symbolic structure 58

7.4. The C*-algebra generated by the reduced normal operator 59

7.5. The C*-algebra B[superscript (a) subscript 0](X, [superscript 0 Omega superscript 1/2]) 62

7.6. The spectrum of the C*-algebra B[superscript (a) subscript 0](X, [superscript 0 Omega superscript 1/2]) 63

Chapter 8. [psi]*-algebras of 0-pseudodifferential operators 69

8.1. Submultiplicative [psi]*-algebras 69

8.2. [psi]*-completions of b-c- and 0-calculus 70

Appendix A. Spaces of conormal functions 73.

Notes:

"Volume 163, number 777 (fourth of 5 numbers)."

Includes bibliographical references and index.

ISBN:

0821832727

OCLC:

51477857