Relative zeta functions, relative determinants and scattering theory

Communications in Mathematical Physics

Volumn 192, Issue 2, 1998, Pages 309-347

  Müller, Werner ^a  

^a UNIVERSITY OF BONN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038294284     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050301     Document Type: Article

References (51)

1. Atiyah, M.F., Patodi, V.K. and I.M. Singer: Spectral asymmetry and Riemannian geometry, I. Math. Proc. Camb. Phil. Soc. 77, 43-69 (1975)
2. Atiyah, M.F., Patodi, V.K. and Singer, I.M.: Spectral asymmetry and Riemannian geometry, III. Math. Proc. Camb. Phil. Soc. 79, 71-99 (1976)
3. Bismut, J.-M. and Cheeger, J.: Families index for manifolds with boundary, super connections, and cones, I. J. Funct. Anal. 90, 306-354 (1990)
4. Bismut, J.-M. and Freed, D.S.: The analysis of elliptic families, I. Metrics and connections on determinant bundles. Commun. Math. Phys. 106, 159-176 (1986)
5. Birman, M.Sh. and Krein, M.G.: On the theory of wave operators and scattering operators. Dokl. Akad. Nauk SSSR 144, 475-478 (1962); English transl. in Soviet Math. Dokl. 3 (1962)
6. Birman, M.Sh. and Krein, M.G.: On the theory of wave operators and scattering operators. Dokl. Akad. Nauk SSSR 144, 475-478 (1962); English transl. in Soviet Math. Dokl. 3 (1962)
7. Bruneau, V.: Propriétés asymptotiques du spectre continu d'opérateurs de Dirac. These de Doctorat, Université de Nantes, 1995
8. Bruneau, V.: Sur le spectre continu de l'opérateur de Dirac: formule de Weyl, limite non-relativiste. C.R. Acad. Sci. Paris 322, 43-48 (1996)
9. Birman, M.Sh. and Yafaev, D.R.: The spectral shift function. The work of M.G. Krein and its further development. St. Petersburg Math. J. 4, 833-870 (1993)
10. Bunke, U.: Relative index theory. J. Funct. Anal. 105, 63-76 (1992)
11. Christiansen, T.: Scattering theory for manifolds with asymptotically cylindrical ends. J. Funct. Anal. 131, 499-530 (1995)
12. Christiansen, T.and Zworski, M.: Spectral asymptotics for manifolds with cylindrical ends. Ann. Inst. Fourier, Grenoble 45, 251-263 (1995)
13. Cotta-Ramusino, P., Krüger, W. and Schrader, R.: Quantum scattering by external metrics and Yang-Mills potentials. Ann. Inst. Henri Poincaré 31, 43-71 (1979)
14. e série, 14, 27-39 (1981)
15. Colin de Verdiere, Y.: Pseudo-Laplaciens II. Ann. Inst. Fourier, Grenoble 33, 87-113 (1983)
16. Deninger, C.: Local L-factors of motives and regularized determinants. Invent, math. 107, 135-151 (1992)
17. Donnelly, H.: Eigenvalue estimates for certain noncompact manifolds. Michigan Math. J. 31, 349-357 (1984)
18. Gilkey, P.B.: Invariance theory, the heat equation, and the Atiyah-Singer index theorem. Second edition, Boca Raton, Ann Arbor: CRC Press, 1995
19. Gamboa Saravi, R.E., Muschietti, M.A., Schaposnik, F.A. and Solomin, J.E.: ζ-function method and the evaluation of fermion currents. J. Math. Phys. 26, 2045-2049 (1985)
20. n. These de 3eme cycle, Grenoble, 1981
21. Guillopé, L.: Asymptotique de la phase de diffusion pour l'opérateur de Schrödinger avec potentiel. C.R. Acad. Sci. Paris 293, 601-603 (1981)
22. Hawking, S.W.: Zeta function regularization of path integrals in curved space time. Commun. Math. Phys. 55, 133-148 (1977)
23. Hejhal, D.A.: The Selberg trace formula and the Riemann zeta function. Duke Math. J. 43, 441-182 (1976)
24. m), m ≥ 5. Duke Math. J. 47, 57-80 (1980)
25. Jensen, A. and Kato, T.: Spectral properties of Schrödinger operators and time-decay of the wave functions. Duke Math. J. 46, 583-611 (1979)
26. Jensen, A. and Kato, T.: Asymptotic behaviour of the scattering phase for exterior domains. Commun. Partial Diff. Equations 3, 1165-1195 (1978)
27. Jorgenson, J. and Lundelius, R.: Continuity of relative hyperbolic spectral theory through metric degeneration. Duke Math. J. 84, 47-81 (1996)
28. Kato, T.: Perturbation theory for linear operators. Berlin: Springer-Verlag, 1966
29. Kato, T.: Wave operators and unitary equivalence. Pacific J. Math. 15, 171-180 (1965)
30. Krein, M.G.: On the trace formula in perturbation theory. Mat. Sbornik 33(75), 597-626 (1953) (Russian)
31. Lundelius, R.: Asymptotics of the determinant of the Laplacian on hyperbolic surfaces of finite volume. Duke Math. J. 71, 211-242 (1993)
32. Melrose, R.B.: The Atiyah-Patodi-Singer index theorem. Boston: A.K. Peters, 1993
33. Melrose, R.B.: Geometric scattering theory. Cambridge: Cambridge University Press, 1995
34. Müller, W.. Spectral theory for Riemannian manifolds with cusps and a related trace formula. Math. Nachrichten 111, 197-288 (1983)
35. Müller, W.: Spectral theory and scattering theory for certain complete surfaces of finite volume. Invent, math. 109, 265-305 (1992)
36. Müller, W.: Eta invariants and manifolds with boundary. J. Diff. Geom. 40, 311-377 (1994)
37. Müller, W. On the analytic continuation of rank one Eisenstein series. Geom. Funct. Anal. 6, 572-586 (1996)
38. Müller, W. Manifolds with cusps of rank one. Lecture Notes in Math. 1244, Berlin: Springer-Verlag, 1987
39. Müller, W.: Relative determinants of elliptic operators and scattering theory. Journees "Equations aux derivees partielles", Saint-Jean-de Monts 1996, Ecole Polyt.
40. Osgood, B., Phillips, R. and Sarnak, P.: Extremals of determiants of Laplacians. J. Funct. Anal. 80, 148-211 (1988)
41. Parnovski, L.B.: Spectral asymptotics of the Laplace operator on surfaces with cusps. Math. Annalen 303, 281-296 (1995)
42. Ray, D.B. and Singer, I.M.: R-torsion and the Laplacian on Riemannian manifolds. Adv. Math. 7, 145-210 (1971)
43. Reed, M. and Simon, B.: Methods of mathematical physics. IV, London: Academic Press, 1978
44. Robert, D.: Asymptotique a grande énergie de la phase de diffusion pour un potentiel. Asymptotic Anal. 3, 301-320 (1991)
45. e série, 25, 107-134 (1992)
46. Sarnak, P.: Arithmetic quantum chaos. Israel Math. Conf. Proc. 8, 183-236 (1995)
47. Seeley, R.T.: Complex powers of an elliptic operator. Proc. Symp. Pure Math. 10, 288-307 (1967)
48. Singer, I.M.: Families of Dirac operators with applications to physics. In: Élie Cartan et les Mathématiques d'aujourd'hui, Astérisque 1985, Numéro Hors Série.
49. Sjöstrand, J. and Zworski, M.. Complex scaling and the distribution of scattering poles. J. Am. Math. Soc. 4, 729-769 (1991)
50. Thaller, B.: The Dirac equation. Texts and Monographs in Physics, Berlin-Heidelberg-New York: Springer-Verlag, 1992
51. Yafaev, D.R.: Mathematical scattering theory. Transl. Math. Monographs, Vol. 105, Princeton, NJ: AMS, 1992