메뉴 건너뛰기




Volumn 2, Issue 4, 2001, Pages 675-711

Semi-classical estimates on the scattering determinant

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0035537073     PISSN: 14240637     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00001049     Document Type: Article
Times cited : (55)

References (39)
  • 1
    • 0007686041 scopus 로고    scopus 로고
    • A perturbation theory for resonances
    • S. Agmon, A perturbation theory for resonances, Comm. Pure Appl. Math. 51, 1255-1309 (1998).
    • (1998) Comm. Pure Appl. Math. , vol.51 , pp. 1255-1309
    • Agmon, S.1
  • 8
    • 0007461448 scopus 로고
    • Prolongement méromorphe de la matrice de scattering pour des probèmes à deux corps à longue portée
    • C. Gérard and A. Martinez, Prolongement méromorphe de la matrice de scattering pour des probèmes à deux corps à longue portée. Ann. Inst. H. Poincaré (Physique Théorique) 51, 81-110 (1989).
    • (1989) Ann. Inst. H. Poincaré (Physique Théorique) , vol.51 , pp. 81-110
    • Gérard, C.1    Martinez, A.2
  • 9
    • 0003301335 scopus 로고
    • Introduction to the theory of linear non-self-adjoint operators
    • A.M.S., Providence
    • I.C. Gohberg and M. G. Krein, Introduction to the Theory of Linear Non-self-adjoint Operators, Translations of Mathematical Monographs 18, A.M.S., Providence, (1969).
    • (1969) Translations of Mathematical Monographs , vol.18
    • Gohberg, I.C.1    Krein, M.G.2
  • 10
    • 84956263391 scopus 로고
    • An operator generalization of the logarithmic residue theorem and the theorem of Rouché
    • I.C. Gohberg and E. I. Sigal, An operator generalization of the logarithmic residue theorem and the theorem of Rouché, Math. USSR Sbornik 13, 603-624 (1971).
    • (1971) Math. USSR Sbornik , vol.13 , pp. 603-624
    • Gohberg, I.C.1    Sigal, E.I.2
  • 11
    • 0031486229 scopus 로고    scopus 로고
    • Scattering asymptotics for Riemann surfaces
    • L. Guillopé and M. Zworski, Scattering asymptotics for Riemann surfaces, Ann. of Math. 129, 597-660 (1997).
    • (1997) Ann. of Math. , vol.129 , pp. 597-660
    • Guillopé, L.1    Zworski, M.2
  • 13
    • 0000736303 scopus 로고
    • Generic simplicity of resonances
    • F. Klopp and M. Zworski, Generic simplicity of resonances, Helv. Phys. Acta 68, 531-538 (1995).
    • (1995) Helv. Phys. Acta , vol.68 , pp. 531-538
    • Klopp, F.1    Zworski, M.2
  • 14
    • 0000179312 scopus 로고
    • Polynomial bound on the number of scattering poles
    • R.B. Melrose, Polynomial bound on the number of scattering poles. J. Funct. Anal. 53, 287-303 (1983).
    • (1983) J. Funct. Anal. , vol.53 , pp. 287-303
    • Melrose, R.B.1
  • 15
    • 33846685553 scopus 로고
    • Weyl asymptotics for the phase in obstacle scattering
    • R.B. Melrose, Weyl asymptotics for the phase in obstacle scattering, Comm. P.D.E., 13, 1431-1439 (1988).
    • (1988) Comm. P.D.E. , vol.13 , pp. 1431-1439
    • Melrose, R.B.1
  • 17
    • 0002570446 scopus 로고
    • Sojourn times of trapping rays and the behavior of the modified resolvent of the Laplacian
    • V. Petkov and L. Stoyanov, Sojourn times of trapping rays and the behavior of the modified resolvent of the Laplacian, Ann. Inst. H. Poincaré (Physique Théorique) 62, 17-45 (1995).
    • (1995) Ann. Inst. H. Poincaré (Physique Théorique) , vol.62 , pp. 17-45
    • Petkov, V.1    Stoyanov, L.2
  • 18
    • 0033241780 scopus 로고    scopus 로고
    • Breit-Wigner approximation and the distribution of resonances
    • V. Petkov and M. Zworski, Breit-Wigner approximation and the distribution of resonances, Commun. Math. Phys. 204, 329-351 (1999).
    • (1999) Commun. Math. Phys. , vol.204 , pp. 329-351
    • Petkov, V.1    Zworski, M.2
  • 20
    • 0002544389 scopus 로고
    • Relative time-delay for perturbations of elliptic operators and semiclassical asymptotics
    • D. Robert, Relative time-delay for perturbations of elliptic operators and semiclassical asymptotics, J. Funct. Anal. 126, 36-82 (1994).
    • (1994) J. Funct. Anal. , vol.126 , pp. 36-82
    • Robert, D.1
  • 21
    • 0000792141 scopus 로고
    • Resonant states and poles of the scattering matrix for perturbations of -Δ
    • N. Shenk and D. Thoe, Resonant states and poles of the scattering matrix for perturbations of -Δ, J. Math. Anal. Appl. 37, 467-491 (1972).
    • (1972) J. Math. Anal. Appl. , vol.37 , pp. 467-491
    • Shenk, N.1    Thoe, D.2
  • 22
    • 0001047998 scopus 로고    scopus 로고
    • A trace formula and review of some estimates for resonances
    • Lucca
    • J. Sjöstrand, A Trace Formula and Review of Some Estimates for Resonances, in Microlocal analysis and spectral theory (Lucca, 1996), 377-437, NATO Adv. Sci. Inst. Ser. C, Math. Phys. Sci., 490, Kluwer Acad. Publ., Dordrecht, (1997).
    • (1996) Microlocal Analysis and Spectral Theory , pp. 377-437
    • Sjöstrand, J.1
  • 23
    • 0003787266 scopus 로고    scopus 로고
    • Kluwer Acad. Publ., Dordrecht
    • J. Sjöstrand, A Trace Formula and Review of Some Estimates for Resonances, in Microlocal analysis and spectral theory (Lucca, 1996), 377-437, NATO Adv. Sci. Inst. Ser. C, Math. Phys. Sci., 490, Kluwer Acad. Publ., Dordrecht, (1997).
    • (1997) NATO Adv. Sci. Inst. Ser. C, Math. Phys. Sci. , pp. 490
  • 24
    • 18044399941 scopus 로고    scopus 로고
    • Resonances for bottles and related trace formulæ
    • J. Sjöstrand, Resonances for bottles and related trace formulæ, Math. Nachr. 221, 95-149 (2001).
    • (2001) Math. Nachr. , vol.221 , pp. 95-149
    • Sjöstrand, J.1
  • 25
    • 84968505435 scopus 로고
    • Complex scaling and the distribution of scattering poles
    • J. Sjöstrand and M. Zworski, Complex Scaling and the Distribution of Scattering Poles, Journal of AMS, 4, 729-769 (4) (1991).
    • (1991) Journal of AMS , vol.4 , Issue.4 , pp. 729-769
    • Sjöstrand, J.1    Zworski, M.2
  • 26
    • 0001226466 scopus 로고
    • Lower bounds on the number of scattering poles
    • J. Sjöstrand and M. Zworski, Lower bounds on the number of scattering poles, Comm. P.D.E. 18, 847-857 (1993).
    • (1993) Comm. P.D.E. , vol.18 , pp. 847-857
    • Sjöstrand, J.1    Zworski, M.2
  • 27
    • 0001031066 scopus 로고
    • Lower bounds on the number of scattering poles, II
    • J. Sjöstrand and M. Zworski, Lower bounds on the number of scattering poles, II, J. Funct. Anal. 123 (4), 336-367 (1994).
    • (1994) J. Funct. Anal. , vol.123 , Issue.4 , pp. 336-367
    • Sjöstrand, J.1    Zworski, M.2
  • 28
    • 0032219326 scopus 로고    scopus 로고
    • From quasimodes to resonances
    • S.H. Tang and M. Zworski, From quasimodes to resonances, Math. Res. Lett., 5, 261-272 (1998).
    • (1998) Math. Res. Lett. , vol.5 , pp. 261-272
    • Tang, S.H.1    Zworski, M.2
  • 29
    • 0034375059 scopus 로고    scopus 로고
    • Resonance expansions of scattered waves
    • S.H. Tang and M. Zworski, Resonance expansions of scattered waves, Comm. Pure Appl. Math. 53, 1305-1334 (2000).
    • (2000) Comm. Pure Appl. Math. , vol.53 , pp. 1305-1334
    • Tang, S.H.1    Zworski, M.2
  • 31
    • 1842660790 scopus 로고    scopus 로고
    • Geometric scattering theory for long-range potentials and metrics
    • A. Vasy, Geometric scattering theory for long-range potentials and metrics, Internat. Math. Res. Notices 6, 285-315 (1998).
    • (1998) Internat. Math. Res. Notices , vol.6 , pp. 285-315
    • Vasy, A.1
  • 32
    • 0002252738 scopus 로고
    • Sharp polynomial bounds on the mumber of scattering poles for perturbations of the Laplacian
    • G. Vodev, Sharp polynomial bounds on the mumber of scattering poles for perturbations of the Laplacian, Commun. Math. Phys. 146, 39-49 (1992).
    • (1992) Commun. Math. Phys. , vol.146 , pp. 39-49
    • Vodev, G.1
  • 33
    • 0001135046 scopus 로고
    • On the distribution of scattering poles for perturbations of the Laplacian
    • G. Vodev, On the distribution of scattering poles for perturbations of the Laplacian, Ann. Inst. Fourier (Grenoble) 42, 625-635 (1992).
    • (1992) Ann. Inst. Fourier (Grenoble) , vol.42 , pp. 625-635
    • Vodev, G.1
  • 34
    • 0030585672 scopus 로고    scopus 로고
    • Asymptotics on the number of scattering poles for degenerate perturbations of the Laplacian
    • G. Vodev, Asymptotics on the number of scattering poles for degenerate perturbations of the Laplacian. J. Funct. Anal. 138, 295-310 (1996).
    • (1996) J. Funct. Anal. , vol.138 , pp. 295-310
    • Vodev, G.1
  • 35
    • 84972578157 scopus 로고
    • Sharp polynomial bounds on the number of scattering poles
    • M. Zworski, Sharp polynomial bounds on the number of scattering poles, Duke Math. J. 59, 311-323 (1989).
    • (1989) Duke Math. J. , vol.59 , pp. 311-323
    • Zworski, M.1
  • 37
    • 0000472636 scopus 로고    scopus 로고
    • Poisson formulæ for resonances in even dimensions
    • M. Zworski, Poisson formulæ for resonances in even dimensions, Asian J. Math. 2 (3), 609-617 (1998).
    • (1998) Asian J. Math. , vol.2 , Issue.3 , pp. 609-617
    • Zworski, M.1
  • 38
    • 0001518892 scopus 로고    scopus 로고
    • Resonances in physics and geometry
    • M. Zworski, Resonances in physics and geometry. Notices Amer. Math. Soc. 46, 319-328 (1999).
    • (1999) Notices Amer. Math. Soc. , vol.46 , pp. 319-328
    • Zworski, M.1
  • 39
    • 0007378728 scopus 로고    scopus 로고
    • Singular part of the scattering matrix determines the obstacle
    • preprint, to appear
    • M. Zworski, Singular part of the scattering matrix determines the obstacle, preprint (1999), Osaka J. Math. to appear.
    • (1999) Osaka J. Math.
    • Zworski, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.