Sjöstrand, Johannes Resonances for bottles and trace formulae. (English) Zbl 0979.35109 Math. Nachr. 221, 95-149 (2001). Author’s abstract: In the first half of the paper, we give a simplified proof of a recent local trace formula for resonances. In the second half we use similar ideas to study resonances near the real axis in bottle like situations. As to the previous results, see J. Sjöstrand and M. Zworski [Commun. Partial Differ. Equations 18, No. 5-6, 847-857 (1993; Zbl 0784.35070); J. Funct. Anal. 123, No. 2, 336-367 (1994; Zbl 0823.35137)]; J. Sjöstrand [NATO ASI Ser., Ser. C, Math. Phys. Sci. 490, 377-437 (1997; Zbl 0877.35090)]; M. Zworski [Asian J. Math. 2, No. 3, 609-618 (1998; Zbl 0932.47004)]. Reviewer: Serghey G.Suvorov (Donetsk) Cited in 1 ReviewCited in 28 Documents MSC: 35P15 Estimates of eigenvalues in context of PDEs 35P25 Scattering theory for PDEs 47A40 Scattering theory of linear operators Keywords:local trace formula; scattering poles Citations:Zbl 0784.35070; Zbl 0823.35137; Zbl 0877.35090; Zbl 0932.47004 × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Aguilar, Comm. Math. Phys. 22 pp 269– (1971) · Zbl 0219.47011 · doi:10.1007/BF01877510 [2] Balslev, Comm. Math. Phys. 22 pp 280– (1971) · Zbl 0219.47005 · doi:10.1007/BF01877511 [3] Bardos, Comm PDE 7 pp 905– (1982) · Zbl 0496.35067 · doi:10.1080/03605308208820241 [4] and : Spectral Asymptotics in the Semi-Classical Limit, London Mathematical Society Lecture Note Series 268, Cambridge University Press, Cambridge, 1999 [5] and : Introduction to the Theory of Nonselfadjoint Operators, Transl. of Math. Monographs 18, AMS, Providence, 1969 [6] : Functional Calculus for Pseudodifferential Boundary Problems, Progress in Math. Vol. 65, 2nd ed., Birkhäuser 1996 [7] Guillopé, Ann. Math. 145 pp 597– (1997) · Zbl 0898.58054 · doi:10.2307/2951846 [8] Helffer, Springer Lecture Notes in Physics 345 pp 118– (1989) · doi:10.1007/3-540-51783-9_19 [9] Helffer, Bull. de la SMF 114 (1986) [10] Melrose, J. Funct. An. 45 pp 429– (1982) · Zbl 0525.47007 · doi:10.1016/0022-1236(82)90003-9 [11] Petkov, Comm. Math. Phys. 204 pp 329– (1999) · Zbl 0936.47004 · doi:10.1007/s002200050648 [12] Popov, Comm. Math. Phys. 196 pp 363– (1998) · Zbl 0924.58100 · doi:10.1007/s002200050425 [13] Popov, Comm. Math. Phys. 207 pp 411– (1999) · Zbl 0951.35036 · doi:10.1007/s002200050731 [14] Popov, Asymptot. Anal. 19 pp 253– (1999) [15] and : Methods of Modern Mathematical Physics, I-IV, Academic Press, New-York, 1978 [16] : A Trace Formula and Review of Some Estimates for Resonances. In: Microlocal Analysis and Spectral Theory, NATO ASI Series C, Vol. 490, p. 377-437, Kluwer, 1997 · Zbl 0877.35090 [17] Sjöstrand, J. of AMS 4 pp 729– (1991) [18] Sjöstrand, Comm. PDE 17 pp 1021– (1992) · Zbl 0766.35031 · doi:10.1080/03605309208820875 [19] Sjöstrand, J. Funct. An. 123 pp 336– (1994) · Zbl 0823.35137 · doi:10.1006/jfan.1994.1092 [20] Sjöstrand, Comm. PDE 18 pp 847– (1993) · Zbl 0784.35070 · doi:10.1080/03605309308820953 [21] Sjöstrand, Acta Math. 183 pp 191– (1999) · Zbl 0989.35099 · doi:10.1007/BF02392828 [22] Stefanov, Duke Math. J. 99 pp 75– (1999) · Zbl 0952.47013 · doi:10.1215/S0012-7094-99-09903-9 [23] Stefanov, Comm. Math. Phys. 176 pp 645– (1996) · Zbl 0851.35032 · doi:10.1007/BF02099253 [24] Tang, Math. Res. Letters 5 pp 261– (1998) · Zbl 0913.35101 · doi:10.4310/MRL.1998.v5.n3.a1 [25] Vodev, Ann. Inst. Fourier 40 pp 625– (1992) · Zbl 0738.35054 · doi:10.5802/aif.1303 [26] Vodev, J. Funct. Anal. 138 pp 295– (1996) · Zbl 0862.35082 · doi:10.1006/jfan.1996.0066 [27] Zworski, Asian J. Math. 2 pp 609– (1998) · Zbl 0932.47004 · doi:10.4310/AJM.1998.v2.n3.a6 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.