Relative determinants of elliptic operators and scattering theory
Journées équations aux dérivées partielles (1996)
- Volume: 1996, page 1-24
- ISSN: 0752-0360
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topMüller, Werner. "Relative determinants of elliptic operators and scattering theory." Journées équations aux dérivées partielles 1996 (1996): 1-24. <http://eudml.org/doc/93320>.
@article{Müller1996,
author = {Müller, Werner},
journal = {Journées équations aux dérivées partielles},
keywords = {zeta function of an operator; survey; relative determinants; elliptic operators; noncompact Riemannian manifolds},
language = {eng},
pages = {1-24},
publisher = {Ecole polytechnique},
title = {Relative determinants of elliptic operators and scattering theory},
url = {http://eudml.org/doc/93320},
volume = {1996},
year = {1996},
}
TY - JOUR
AU - Müller, Werner
TI - Relative determinants of elliptic operators and scattering theory
JO - Journées équations aux dérivées partielles
PY - 1996
PB - Ecole polytechnique
VL - 1996
SP - 1
EP - 24
LA - eng
KW - zeta function of an operator; survey; relative determinants; elliptic operators; noncompact Riemannian manifolds
UR - http://eudml.org/doc/93320
ER -
References
top- [APS] M.F. Atiyah, V.K. Patodi and I.M. Singer, Spectral asymmetry and Riemannian geometry, I, Math. Proc. Camb. Phil. Soc. 77 (1975), 43-69. Zbl0297.58008MR53 #1655a
- [BK] M.Sh. Birman and M.G. Krein, On the theory of wave operators and scattering operators, Dokl. Akad. Nauk SSSR 144 (1962), 475-478 ; English transl. in Soviet Math. Dokl. 3 (1962). Zbl0196.45004
- [Br] V. Bruneau, Propriétés asymptotiques du spectre continu d'opérateurs de Dirac, These de Doctorat, Université de Nantes, 1995.
- [BY] M.Sh. Birman and M.G. Krein, The spectral shift function. The work of M.G. Krein and its further development, St. Petersburg Math. J. 4 (1993), 833-870. Zbl0791.47013
- [BC] J.-M. Bismut and J. Cheeger, Families index for manifolds with boundary, super connections, and cones, I, Journal Funct. Analysis 90 (1990), 306-354. Zbl0711.53023MR91e:58181
- [BF1] J.-M. Bismut and D.S. Freed, The analysis of elliptic families, I. Metrics and connections on determinant bundles, Commun. Math. Phys. 106 (1986), 159-176. Zbl0657.58037MR88h:58110a
- [BF2] J.-M. Bismut and D.S. Freed, The analysis of elliptic families, II, Commun. Math. Phys. 107 (1986), 103-163. Zbl0657.58038MR88h:58110b
- [BGS1] J.-M. Bismut, H. Gillet and C. Soulé, Analytic torsion and holomorphic determinant bundles, I. Bott-chern forms and analytic torsion, Commun. Math. Phys. 115 (1988), 49-78. Zbl0651.32017MR89g:58192a
- [BGS2] J.-M. Bismut, H. Gillet and C. Soulé, Analytic torsion and holomorphic determinant bundles, II. Direct images and Bott-Chern forms, Commun. Math. Phys. 115 (1988), 79-126. Zbl0651.32017MR89g:58192b
- [BGS3] J.-M. Bismut, H. Gillet and C. Soulé, Analytic torsion and holomorphic determinant bundles, III. Quillen metric on holomorphic determinants, Commun. Math. Phys. 115 (1988), 301-351. Zbl0651.32017MR89g:58192c
- [BL] J.-M. Bismut and G. Lebeau, Complex immersions and Quillen metrics, Publications Math. 74 (1991), 1-298. Zbl0784.32010MR94a:58205
- [BZ] J.-M. Bismut and W. Zhang, An extension of a theorem by Cheeger and Müller, Astérisque 205 (1992). Zbl0781.58039
- [BCY] T.P. Branson, S.-Y. A. Chang, and P.C. Yang, Estimates and extremals for zeta function determinants on four-manifolds, Commun. Math. Phys. 149 (1992), 241-262. Zbl0761.58053MR93m:58116
- [BFK] D. Burghelea, L. Friedlander, T. Kappeler, and P. McDonald, Analytic and Reidemeister torsion for representations in finite type Hilbert modules, Preprint, Ohio State University, 1996. Zbl0874.57025MR97i:58177
- [C] J. Cheeger, Analytic torsion and the heat equation, Annals of Math. 109 (1979), 259-322. Zbl0412.58026MR80j:58065a
- [CV1] Y. Colin de Verdiere, Une formule de traces pour l'opérateur de Schrödinger dans ℝ3, Ann. scient. Éc. Norm. Sup., 4e série, 14 (1981), 27-39. Zbl0482.35068MR82g:35088
- [CV2] Y. Colin de Verdiere, Pseudo-Laplaciens II, Ann. Inst. Fourier, Grenoble 33 (1983), 87-113. Zbl0496.58016MR84k:58222
- [De] C. Deninger, Local L-factors of motives and regularized determinants, Invent. math. 107 (1992), 135-151. Zbl0762.14015MR93a:11056
- [Do] S.K. Donaldson, Infinite determinants, stable bundles, and curvature, Duke Math. J. 54 (1987), 231-247. Zbl0627.53052MR88g:32046
- [Fa] G. Faltings, Lectures on the arithmetic Riemann-Roch theorem, Ann. Math. Studies 127 (1992). Zbl0744.14016MR93f:14006
- [Fr] D.S. Freed, Determinants, torsion, and strings. Commun. Math. Phys. 107 (1986), 483-513. Zbl0606.58013MR88b:58130
- [GMS] R.E. Gamboa Saravi, M.A. Muschietti, F.A. Schaposnik, and J.E. Solomin, ζ-function method and the evaluation of fermion currents, J. Math. Phys. 26 (1985), 2045-2049. MR87e:81137
- [GS] H. Gillet and Ch. Soullé, An arithmetic Riemann-Roch theorem, Invent. math. 110 (1992), 473-543. Zbl0777.14008MR94f:14019
- [Gu1] L. Guillopé, Une formule de trace pour l'opérateur de Schrödinger dans ℝn, These de 3eme cycle, Grenoble, 1981.
- [Gu2] L. Guillopé, Asymptotique de la phase de diffusion pour l'opérateur de Schrödinger avec potentiel, C.R. Acad. Sci. Paris 293 (1981), 601-603. Zbl0487.35073MR83a:35079
- [H] S.W. Hawking, Zeta function regularization of path integrals in curved space time, Commun. Math. Phys. 55 (1977), 133-148. Zbl0407.58024MR58 #25823
- [He] D.A. Hejhal, The Selberg trace formula and the Riemann zeta function, Duke Math. J. 43 (1976), 441-482. Zbl0346.10010MR54 #2591
- [JK] A. Jensen and T. Kato, Spectral properties of Schrödinger operators and time-decay of the wave functions, Duke Math. J. 46 (1979), 583-611. Zbl0448.35080MR81b:35079
- [J] A. Jensen, Spectral properties of Schrödinger operators and time-decay of the wave functions, results in L2 (ℝm), m ≥ 5, Duke Math. J. 47 (1980), 57-80. Zbl0437.47009MR81e:35092
- [K] T. Kato, Perturbation theory for linear operators, Springer-Verlag, Berlin, 1966. Zbl0148.12601MR34 #3324
- [KV] M. Kontsevich and S. Vishik, Determinants of elliptic pseudo-differential operators, MPI-Preprint Nr. 94-30, Bonn, 1994.
- [Lo] J. Lott, Heat kernels on covering spaces and topological invariants, J. Diff. Geometry 35 (1992), 471-510. Zbl0770.58040MR93b:58140
- [Me] R.B. Melrose, The Atiyah-Patodi-Singer index theorem, A.K. Peters, Boston, 1993. Zbl0796.58050MR96g:58180
- [Mu1] W. Müller, Spectral theory for Riemannian manifolds with cusps and a related trace formula, Math. Nachrichten 111 (1983), 197-288. Zbl0529.58035MR85i:58121
- [Mu2] W. Müller, Spectral theory and scattering theory for certain complete surfaces of finite volume, Invent. math. 109 (1992), 265-305. Zbl0772.58063
- [Mu3] W. Müller, Analytic torsion and R-torsion of Riemannian manifolds, Adv. in Math. 28 (1978), 233-305. Zbl0395.57011MR80j:58065b
- [Mu4] W. Müller, Analytic torsion and R-torsion for unimodular representations, J. Amer. Math. Soc. 6 (1993), 721-753. Zbl0789.58071MR93m:58119
- [Mu5] W. Müller, Relative zeta functions, relative determinants, and scattering theory, in preparation. Zbl0947.58025
- [O] K. Okikiolu, The multiplicative anomaly for determinants of elliptic operators, Duke Math. J. 79 (1995), 723-750. Zbl0851.58048MR96j:58176
- [OPS1] B. Osgood, R. Phillips, and P. Sarnak, Extremals of determiants of Laplacians, J. Funct. Anal. 80 (1988), 148-211. Zbl0653.53022MR90d:58159
- [OPS2] B. Osgood, R. Phillips, and P. Sarnak, Compact isospectral sets of surfaces, J. Funct. Anal. 80 (1988), 212-234. Zbl0653.53021MR90d:58160
- [Pa] L.B. Parnovski, Spectral asymptotics of the Laplace operator on surfaces with cusps, Math. Annalen 303 (1995), 281-296. Zbl0849.35093MR97a:11080
- [Ro] D. Robert, Asymptotique a grande énergie de la phase de diffusion pour un potentiel, Asymptotic Analysis, 3 (1991), 301-320. Zbl0737.35054MR91m:35179
- [RS1] D.B. Ray and I.M. Singer, R-torsion and the Laplacian on Riemannian manifolds, Advances in Math. 7 (1971), 145-210. Zbl0239.58014MR45 #4447
- [RS2] D.B. Ray and I.M. Singer, Analytic torsion for complex manifolds, Annals of Math. 98 (1973), 154-177. Zbl0267.32014MR52 #4344
- [Sa] P. Sarnak, Arithmetic quantum chaos, Israel Math. Conf. Proc. 8 (1995), 183-236. Zbl0831.58045MR96d:11059
- [S] R.T. Seeley, Complex powers of an elliptic operator, Proc. Symp. Pure Math. 10 (1967), 288-307. Zbl0159.15504MR38 #6220
- [Si] I.M. Singer, Families of Dirac operators with applications to physics, In : Élie Cartan et les Mathématiques d'aujourd'hui, Astérisque 1985, Numéro Hors Série. Zbl0603.58054MR88a:58192
- [Y] D.R. Yafaev, Mathematical scattering theory, Translations of Mathematical Monographs, Vol. 105 (1992), AMS. Zbl0761.47001MR94f:47012
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