Déterminant relatif et la fonction Xi
Séminaire de théorie spectrale et géométrie, Tome 18 (1999-2000), pp. 119-124.
@article{TSG_1999-2000__18__119_0,
     author = {Carron, Gilles},
     title = {D\'eterminant relatif et la fonction {Xi}},
     journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie},
     pages = {119--124},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {18},
     year = {1999-2000},
     mrnumber = {1812216},
     zbl = {0981.58024},
     language = {fr},
     url = {http://archive.numdam.org/item/TSG_1999-2000__18__119_0/}
}
TY  - JOUR
AU  - Carron, Gilles
TI  - Déterminant relatif et la fonction Xi
JO  - Séminaire de théorie spectrale et géométrie
PY  - 1999-2000
SP  - 119
EP  - 124
VL  - 18
PB  - Institut Fourier
PP  - Grenoble
UR  - http://archive.numdam.org/item/TSG_1999-2000__18__119_0/
LA  - fr
ID  - TSG_1999-2000__18__119_0
ER  - 
%0 Journal Article
%A Carron, Gilles
%T Déterminant relatif et la fonction Xi
%J Séminaire de théorie spectrale et géométrie
%D 1999-2000
%P 119-124
%V 18
%I Institut Fourier
%C Grenoble
%U http://archive.numdam.org/item/TSG_1999-2000__18__119_0/
%G fr
%F TSG_1999-2000__18__119_0
Carron, Gilles. Déterminant relatif et la fonction Xi. Séminaire de théorie spectrale et géométrie, Tome 18 (1999-2000), pp. 119-124. http://archive.numdam.org/item/TSG_1999-2000__18__119_0/

[BK] M.Sh Birman, M.G. Krein, on the theory of wave operators and scattering operators, Dokl. Akad. Nauk SSSR, 144 ( 1962), 475-478 ; traduction anglaise in Soviet. Math. Dokl, 3 ( 1962). | MR | Zbl

[B-Y] M.Sh Birman, D.R. Yafaev, The spectral shift fonction, the work of M.G. Krein and its further development, St. Petersburg Math. J., 4 ( 1993), no 5, 833-870. | MR | Zbl

[B] U. Bunke, Relative Index theory, J. Funct. Anal, 105 ( 1992), 63-76. | MR | Zbl

[B-F-K] D. Burghelea, L. Friedlander, T. Kappeler, Mayer-Vietoris formula for determinants of elliptic operators, J. Funct. Anal, 107 ( 1992) 34-65. | MR | Zbl

[Bu] V.S. Buslaev, Scattered plane waves, spectral asymptotics and trace formulae in exterior problems. Dokl Akad. Nauk SSSR 197 ( 1971) 999-1002 ; traduction anglaise Soviet Math. Dokl, 12 ( 1971),591 -595]. | MR | Zbl

[C-Z] T. Christiansen, M. Zworski, Spectral asymptotics for manifolds with cylindrical ends, Ann. Inst. Fourier (Grenoble),45, ( 1995), 251-263. | Numdam | MR | Zbl

[C1] T. Christiansen, Spectral asymptotics for compactly supported perturbations of the Laplacian on Rn, Comm. Partial Differential Equations, 23 ( 1998), n° 5-6, 933-948. | MR | Zbl

[C2] T. Christiansen, Weyl asymptotics for the laplacian on asymtoticalty euclidean spaces, American J. of Math., 121 ( 1999),1-22. | MR | Zbl

[CdV] Y. Colin De Verdière, Une formule de trace pour l'opérateur de Schrödinger dans R3, Ann. Sci.École Norm. Sup., 4 ( 1981), 27-39. | Numdam | MR | Zbl

[F] R. Forman, Functional determinants and geometry, Invent. Math., 88 ( 1987) 447-493. | MR | Zbl

[Gu] L. Guillopé, Asymptotique de la phase de diffusion pour l'opérateur de Schrödinger avec potentiel. C. R. Acad. Sci. Paris Sér. 1 Math., 293 ( 1981), n° 12, 601-603. | MR | Zbl

[G-Z] L. Guillopé, M. Zworski, Scattering asymptotics for Riemann surfaces, Ann. of Math., 145 ( 1997), 597-660. | MR | Zbl

[H-Z] A. Hassell, S. Zelditch, Determinants of laplacians in exterior domains, IMRN, ( 1999), n° 18, pp 971-1004. | MR | Zbl

[J-K] A. Jensen, T. Kato, Asymptotics behaviour of the scattering phase for exterior domains, Comm. Partial Differential Equations, 3 ( 1978), 1165-1195. | MR | Zbl

[K1] M.G. Kron, On the trace formula in perturbation theory, Mat. Sb., 75 ( 1953), 597-626. | MR

[K2] M.G. Krein, On perturbation determinants and the trace formula for unitary andselfadjoint operators. Dokl. Akad. Nauk SSSR 144 ( 1962), 268-271 ; traduction anglaise in Soviet. Math. Dokl., 3 ( 1962). | MR | Zbl

[L-S] S. Levit, U. Smiiansky, A theorem on infinité products of eigenvalues of Sturm type operators, Proc. Amer. Math. Soc., 65, ( 1977), 299-303. | MR | Zbl

[M-R] A. Majda, J. Ralston, An analogue of Weyl's theorem for unbounded domains, I, II, III, Duke Math. J., 45 ( 1978), 183-196, 513-536; 46 ( 1979), n° 4,725-731. | MR | Zbl

[Me] R. Melrose, Weyl asymptotics for the phase in obstacle scattering, Comm. Partial Differential Equations, 13 ( 1988), 1431-1439. | MR | Zbl

[Mu 1] W. Müller, Spectral geometry and scattering theory for certain complete surfaces offinite volume, Invent. Math., 109, ( 1992), 265-305. | MR | Zbl

[Mu 2] W. Müller, Relative zeta functions, relative determinants and scattering theory, Comm. Math. Phys., 192 ( 1998), n° 2, 309-347 | MR | Zbl

[P1] L. B. Parnovski, Spectral asymptotics of the Laplace operator on manifolds with cylindrical ends. Internat. J. Math., 6 ( 1995), n° 6, 911-920. | MR | Zbl

[P2] L.B. Parnovski, Spectral asymptotics of Laplace operators on surfaces with cusps. Math. Ann., 303 ( 1995), n° 2, 281-296. | MR | Zbl

[P-P] V. Petkov, G. Popov, Asymptotic behavior of the scattering phase for non-trapping obstacles, Ann. Inst. Fourier (Grenoble), 32 ( 1982), 111-149. | Numdam | MR | Zbl

[R-S] D.B. Ray, I.M. Singer, R-torsion and the Laplacian on Riemannian manifolds. Advances in Math., 7 ( 1971), 145-210. | MR | Zbl

[R] D. Robert, Sur la formule de Weyls pour les ouverts non-bornés, C. R. Acad. Sci. Paris Sér. I Math., 319 ( 1994), 29-34. | MR | Zbl