Traces on algebras of parameter dependent pseudodifferential operators and the eta-invariant

Transactions of the American Mathematical Society

Volumn 352, Issue 11, 2000, Pages 4911-4936

  Lbsch, Matthias ^a   Pflaum, Markus J ^a  

^a The University of Arizona   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 23044524723     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (20)

1. N. BERLINE, E. GETZLER AND M. VERGNE: Heat kernels and Dirac operators. Grundlehren der Mathematischen Wissenschaften, vol. 298, Springer-Verlag, Berlin-Heidelberg-New York, 1992. MR94e:58130
2. R. BOTT AND L. W. Tu: Differential forms in algebraic topology. Springer-Verlag, BerlinHeidelberg-New York, 1982. MR 83i:57016
3. A. CONNES: Noncömmutative geometry. Academic Press, San Diego, 1994. MR 95j:46063
4. J. J. DuiSTERMAAT: Fourier Integral Operators. Birkhäuser, Basel, 1996. MR 96m:58245
5. P. B. GILKEY: Invariance theory, the heat-equation, and the Atiyah-Singer index theorem second ed., CRC Press, Boca Raton, 1995. MR 98b:58156
6. A. GRIGIS AND J. SJ0STRAND: Microlocal Analysis for Differential Operators. London Mathematical Society Lecture Note Series, vol. 196, Cambridge University Press, 1994. MR 95d:35009
7. G. GRUBB AND R. T. SEELEY: Weakly parametric pseudodifferential operators and Atiyah Patodi-Singer boundary problems. Invent. Math. 121 (1995), 481-529. MR 95k:58216
8. V. GUILLEMIN: A new proof of Weyl's formula on the asymptotic distribution of eigenvalues Adv. in Math. 55 (1985), 131-160. MR 86i:58135
9. M. KONTSEVICH AND S. VlSHlK: Determinants of elliptic pseudo-differential operators Preprint, 1994
10. M. KONTSEVICH AND S. VlSHlK: Geometry of determinants of elliptic operators. In: Functional analysis on the eve of the 21st century. Volume I (S. Gindikin et al., editor). In honor of the eightieth birthday of I. M. Gelfand. Proceedings of the conference, held at Rutgers University, New Brunswick, NJ, October 24-27, 1993. Boston: Birkhäuser, Prog. Math. 131, 173-197 (1995). MR 96m:58264
11. H. B. LAWSON AND M. L. MICHELSOHN: Spin geometry. Princeton University Press, Princeton, NJ, 1989. MR 91g:53001
12. M. LESCII: On the noncommutative residue for pseudodifferential operators with log polyhomogeneous symbols. Ann. Global Anal. Geom 17 (1999), 151-187. CMP 99:09
13. M. LESCH: Operators of Fuchs type, conical singularities, and asymptotic methods. Teubne Texte zur Mathematik, vol. 136, B. G. Teubner, Leipzig, 1997. MR 98d:58174
14. M. LESCII AND J. TOLKSDORF: On the determinant of one-dimensional elliptic boundar value problems. SFB Commun. Math. Phys. 193 (1998), 643-660. CMP 98:13
15. R. B. MELROSE: The eta invariant and families of pseudodifferential operators. Math. Res Lett. 2 (1995), 541-561. MR 96h:58169
16. R.B. MELROSE AND V. NISTOR: C'-algebras of B-pseudodifferential operators and anRk equivariant index theorem. Preprint, 1996; funct-an/9610003 .
17. R.B. MELROSE AND V. NISTOR: Homology of pseudodifferential operators I. Manifolds wit boundary. Preprint, 1996; funct-an/9606005.
18. R.B. MELROSE AND V. NISTOR: In preparation
19. M. A. SHUBIN: Pseudodifferential Operators and Spectral Theory. Springer-Verlag, BerlinHeidelberg-New York, 1987. MR 88c:47105
20. M. WODZICKI: Noncömmutative residue I: Fundamentals, K-Theory. LNM 1289, SpringerVerlag, Berlin-Heidelberg-New York, 1987. MR 90a:58175