Werner Müller. Relative determinants of elliptic operators and scattering theory. Journées équations aux dérivées partielles (1996), article no. 13, 24 p.. doi: 10.5802/jedp.506
@incollection{JEDP_1996____A13_0,
author = {Werner M\"uller},
title = {Relative determinants of elliptic operators and scattering theory},
booktitle = {},
series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
eid = {13},
pages = {1--24},
year = {1996},
publisher = {\'Ecole polytechnique},
doi = {10.5802/jedp.506},
zbl = {0920.58062},
language = {en},
url = {https://proceedings.centre-mersenne.org/articles/10.5802/jedp.506/}
}
TY - JOUR AU - Werner Müller TI - Relative determinants of elliptic operators and scattering theory JO - Journées équations aux dérivées partielles PY - 1996 SP - 1 EP - 24 PB - École polytechnique UR - https://proceedings.centre-mersenne.org/articles/10.5802/jedp.506/ DO - 10.5802/jedp.506 LA - en ID - JEDP_1996____A13_0 ER -
%0 Journal Article %A Werner Müller %T Relative determinants of elliptic operators and scattering theory %J Journées équations aux dérivées partielles %] 13 %D 1996 %P 1-24 %I École polytechnique %U https://proceedings.centre-mersenne.org/articles/10.5802/jedp.506/ %R 10.5802/jedp.506 %G en %F JEDP_1996____A13_0
[APS] , and , Spectral asymmetry and Riemannian geometry, I, Math. Proc. Camb. Phil. Soc. 77 (1975), 43-69. | MR | Zbl
[BK] and , 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). | Zbl
[Br] , Propriétés asymptotiques du spectre continu d'opérateurs de Dirac, These de Doctorat, Université de Nantes, 1995.
[BY] and , The spectral shift function. The work of M.G. Krein and its further development, St. Petersburg Math. J. 4 (1993), 833-870. | Zbl
[BC] and , Families index for manifolds with boundary, super connections, and cones, I, Journal Funct. Analysis 90 (1990), 306-354. | MR | Zbl
[BF1] and , The analysis of elliptic families, I. Metrics and connections on determinant bundles, Commun. Math. Phys. 106 (1986), 159-176. | MR | Zbl
[BF2] and , The analysis of elliptic families, II, Commun. Math. Phys. 107 (1986), 103-163. | MR | Zbl
[BGS1] , and , Analytic torsion and holomorphic determinant bundles, I. Bott-chern forms and analytic torsion, Commun. Math. Phys. 115 (1988), 49-78. | MR | Zbl
[BGS2] , and , Analytic torsion and holomorphic determinant bundles, II. Direct images and Bott-Chern forms, Commun. Math. Phys. 115 (1988), 79-126. | MR | Zbl
[BGS3] , and , Analytic torsion and holomorphic determinant bundles, III. Quillen metric on holomorphic determinants, Commun. Math. Phys. 115 (1988), 301-351. | MR | Zbl
[BL] and , Complex immersions and Quillen metrics, Publications Math. 74 (1991), 1-298. | Numdam | MR | Zbl
[BZ] and , An extension of a theorem by Cheeger and Müller, Astérisque 205 (1992). | Zbl
[BCY] , , and , Estimates and extremals for zeta function determinants on four-manifolds, Commun. Math. Phys. 149 (1992), 241-262. | MR | Zbl
[BFK] , , , and , Analytic and Reidemeister torsion for representations in finite type Hilbert modules, Preprint, Ohio State University, 1996. | MR | Zbl
[C] , Analytic torsion and the heat equation, Annals of Math. 109 (1979), 259-322. | MR | Zbl
[CV1] , Une formule de traces pour l'opérateur de Schrödinger dans ℝ3, Ann. scient. Éc. Norm. Sup., 4e série, 14 (1981), 27-39. | Numdam | MR | Zbl
[CV2] , Pseudo-Laplaciens II, Ann. Inst. Fourier, Grenoble 33 (1983), 87-113. | Numdam | MR | Zbl
[De] , Local L-factors of motives and regularized determinants, Invent. math. 107 (1992), 135-151. | MR | Zbl
[Do] , Infinite determinants, stable bundles, and curvature, Duke Math. J. 54 (1987), 231-247. | MR | Zbl
[Fa] , Lectures on the arithmetic Riemann-Roch theorem, Ann. Math. Studies 127 (1992). | MR | Zbl
[Fr] , Determinants, torsion, and strings. Commun. Math. Phys. 107 (1986), 483-513. | MR | Zbl
[GMS] , , , and , ζ-function method and the evaluation of fermion currents, J. Math. Phys. 26 (1985), 2045-2049. | MR
[GS] and , An arithmetic Riemann-Roch theorem, Invent. math. 110 (1992), 473-543. | MR | Zbl
[Gu1] , Une formule de trace pour l'opérateur de Schrödinger dans ℝn, These de 3eme cycle, Grenoble, 1981.
[Gu2] , Asymptotique de la phase de diffusion pour l'opérateur de Schrödinger avec potentiel, C.R. Acad. Sci. Paris 293 (1981), 601-603. | MR | Zbl
[H] , Zeta function regularization of path integrals in curved space time, Commun. Math. Phys. 55 (1977), 133-148. | MR | Zbl
[He] , The Selberg trace formula and the Riemann zeta function, Duke Math. J. 43 (1976), 441-482. | MR | Zbl
[JK] and , Spectral properties of Schrödinger operators and time-decay of the wave functions, Duke Math. J. 46 (1979), 583-611. | MR | Zbl
[J] , 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. | MR | Zbl
[K] , Perturbation theory for linear operators, Springer-Verlag, Berlin, 1966. | MR | Zbl
[KV] and , Determinants of elliptic pseudo-differential operators, MPI-Preprint Nr. 94-30, Bonn, 1994.
[Lo] , Heat kernels on covering spaces and topological invariants, J. Diff. Geometry 35 (1992), 471-510. | MR | Zbl
[Me] , The Atiyah-Patodi-Singer index theorem, A.K. Peters, Boston, 1993. | MR | Zbl
[Mu1] , Spectral theory for Riemannian manifolds with cusps and a related trace formula, Math. Nachrichten 111 (1983), 197-288. | MR | Zbl
[Mu2] , Spectral theory and scattering theory for certain complete surfaces of finite volume, Invent. math. 109 (1992), 265-305. | Zbl
[Mu3] , Analytic torsion and R-torsion of Riemannian manifolds, Adv. in Math. 28 (1978), 233-305. | MR | Zbl
[Mu4] , Analytic torsion and R-torsion for unimodular representations, J. Amer. Math. Soc. 6 (1993), 721-753. | MR | Zbl
[Mu5] , Relative zeta functions, relative determinants, and scattering theory, in preparation. | Zbl
[O] , The multiplicative anomaly for determinants of elliptic operators, Duke Math. J. 79 (1995), 723-750. | MR | Zbl
[OPS1] , , and , Extremals of determiants of Laplacians, J. Funct. Anal. 80 (1988), 148-211. | MR | Zbl
[OPS2] , , and , Compact isospectral sets of surfaces, J. Funct. Anal. 80 (1988), 212-234. | MR | Zbl
[Pa] , Spectral asymptotics of the Laplace operator on surfaces with cusps, Math. Annalen 303 (1995), 281-296. | MR | Zbl
[Ro] , Asymptotique a grande énergie de la phase de diffusion pour un potentiel, Asymptotic Analysis, 3 (1991), 301-320. | MR | Zbl
[RS1] and , R-torsion and the Laplacian on Riemannian manifolds, Advances in Math. 7 (1971), 145-210. | MR | Zbl
[RS2] and , Analytic torsion for complex manifolds, Annals of Math. 98 (1973), 154-177. | MR | Zbl
[Sa] , Arithmetic quantum chaos, Israel Math. Conf. Proc. 8 (1995), 183-236. | MR | Zbl
[S] , Complex powers of an elliptic operator, Proc. Symp. Pure Math. 10 (1967), 288-307. | MR | Zbl
[Si] , Families of Dirac operators with applications to physics, In : Élie Cartan et les Mathématiques d'aujourd'hui, Astérisque 1985, Numéro Hors Série. | MR | Zbl
[Y] , Mathematical scattering theory, Translations of Mathematical Monographs, Vol. 105 (1992), AMS. | MR | Zbl
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