Zeta and eta functions for Atiyah-Patodi-Singer operators

Journal of Geometric Analysis

Volumn 6, Issue 1, 1996, Pages 31-77

  Grubb, Gerd ^a   Seeley, Robert T ^b  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

^b UNIVERSITY OF MASSACHUSETTS BOSTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 8744244427     PISSN: 10506926     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02921566     Document Type: Article

References (17)

1. [APS] Atiyah, M. F., Patodi, V. K., and Singer, I. M. Spectral asymmetry and Riemannian geometry, I. Math. Proc. Camb. Phil. Soc. 77, 43-69 (1975).
2. [BF] Bismut, J.-M., and Freed, D. S. The analysis of elliptic families, II. Comm. Pure Appl. Math. 107, 103-163 (1986).
3. [B] Bourbaki, N. Fonctions d'une variable réelle. Vol. IV, Ed. Hermann, Paris, 1951.
4. [BG] Branson, T. P., and Gilkey, P. B. Residues of the eta function for an operator of Dirac type. J. Fund. Analysis 108, 47-87 (1992).
5. [DG] Duistermaat, J. J., and Guillemin, V. W. The spectrum of positive elliptic operators and periodic bicharacteristics. Inventiones Math. 29, 39-79 (1975).
6. [DW] Douglas, R. G., and Wojciechowski, K. P. Adiabatic limits of the η-invariants, the odd dimensional Atiyah-Patodi-Singer problem. Comm. Math. Phys. 142, 139-168 (1991)
7. [GiS] Gilkey, P. B., and Smith, L. The eta invariant for a class of elliptic boundary value problems. Comm. Pure Appl. Math. 36, 85-131 (1983).
8. [Gre] Greiner, P. An asymptotic expansion for the heat equation. Arch. Rat. Mech. Anal. 41, 163-218 (1971).
9. [G1] Grubb, G. Functional Calculus of Pseudo-Differential Boundary Problems, Progress in Math. Vol. 65, Birkhäuser, Boston, 1986. Second Edition 1996.
10. [G2] Grubb, G. Heat operator trace expansions and index for general Atiyah-Patodi-Singer boundary problems. Comm. Part. Diff. Equ. 17, 2031-2077 (1992).
11. [GS1] Grubb, G., and Seeley, R. T. Weakly parametric pseudodifferential operators and Atiyah-Patodi-Singer boundary problems. Inventiones Math. 121, 481-529 (1995).
12. [GS2] Grubb, G., and Seeley, R. T. Développements asymptotiques pour l'opérateur d'Atiyah-Patodi-Singer. C. R. Acad. Sci. Paris 317, 1123-1126 (1993).
13. Melrose, R. B. The Atiyah-Patodi-Singer Index Theorem. A. K. Peters Ltd, Wellesley, MA, 1993.
14. [MP] Minakshisundaram, S., and Pleijel, A. Some properties of the eigenfunctions of the Laplace operator on Riemannian manifolds. Canail. J. Math. 1, 242-256 (1949).
15. [S] Seeley, R. T. Complex powers of an elliptic operator. AMS Proc. Symp. Pure Math. X, 1966. Amer. Math. Soc., Providence, pp. 288-307, 1967.
16. [Sh] Shubin, M. A. Pseudodifferential Operators and Spectral Theory. Springer Verlag, Heidelberg, 1978.
17. [Si] Singer, I. M. The n-invariant and the index. Mathematical Aspects of String Theory. (S.-T. Yau, ed.). World Scientific Press, Singapore, pp. 239-258, 1988.