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Volumn 145, Issue 3, 1997, Pages 597-660

Scattering asymptotics for Riemann surfaces

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EID: 0031486229     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.2307/2951846     Document Type: Article
Times cited : (117)

References (73)
  • 1
    • 84990604696 scopus 로고
    • Spectral theory of Schrödinger operators on Euclidean and non-Euclidean spaces
    • SH. AGMON, Spectral theory of Schrödinger operators on Euclidean and non-Euclidean spaces, Comm. Pure Appl. Math. 39 (1986), S3-S16.
    • (1986) Comm. Pure Appl. Math. , vol.39
    • Agmon, Sh.1
  • 3
    • 0000647760 scopus 로고
    • La relation de Poisson pour l'équation des ondes dans un ouvert non borné
    • C. BARDOS, J.-C. GUILLOT, AND J. V. RALSTON, La relation de Poisson pour l'équation des ondes dans un ouvert non borné, Comm. Partial Diff. Eq. 7 (1982), 905-958.
    • (1982) Comm. Partial Diff. Eq. , vol.7 , pp. 905-958
    • Bardos, C.1    Guillot, J.-C.2    Ralston, J.V.3
  • 4
    • 0001537405 scopus 로고
    • Transplantation et isospectralité. I
    • P. BÉRARD, Transplantation et isospectralité. I, Math. Ann. 292 (1992), 547-560.
    • (1992) Math. Ann. , vol.292 , pp. 547-560
    • Bérard, P.1
  • 5
    • 0000678128 scopus 로고
    • Scattering plane waves, spectral asymptotics and trace formulas in exterior problems
    • V. BUSLAEV, Scattering plane waves, spectral asymptotics and trace formulas in exterior problems, Dokl. Akad. Nauk SSSR 197 (1971), 999-1002.
    • (1971) Dokl. Akad. Nauk SSSR , vol.197 , pp. 999-1002
    • Buslaev, V.1
  • 6
    • 0000299136 scopus 로고
    • Spectral asymptotics for manifolds with cylindrical ends
    • Grenoble
    • T. CHRISTIANSEN AND M. ZWORSKI, Spectral asymptotics for manifolds with cylindrical ends, Ann. Inst. Fourier (Grenoble) 45 (1995), 251-263.
    • (1995) Ann. Inst. Fourier , vol.45 , pp. 251-263
    • Christiansen, T.1    Zworski, M.2
  • 7
    • 0002174063 scopus 로고
    • Pseudo-laplaciens II
    • Grenoble
    • Y. COLIN DE VERDIÈRE, Pseudo-laplaciens II, Ann. Inst. Fourier (Grenoble) 33, 2 (1983), 87-113.
    • (1983) Ann. Inst. Fourier , vol.33 , Issue.2 , pp. 87-113
    • Colin De Verdière, Y.1
  • 8
    • 0041151698 scopus 로고
    • Théorie spectrale des surfaces de Riemann d'aire infinie
    • _, Théorie spectrale des surfaces de Riemann d'aire infinie, Astérisque 132 (1985), 259-275.
    • (1985) Astérisque , vol.132 , pp. 259-275
  • 9
    • 0039964587 scopus 로고
    • Lower bounds on the number of scattering poles under lines parallel to the real axis
    • L. FARHY, Lower bounds on the number of scattering poles under lines parallel to the real axis, Comm. Partial Diff. Eq. 20 (1995), 729-740.
    • (1995) Comm. Partial Diff. Eq. , vol.20 , pp. 729-740
    • Farhy, L.1
  • 10
    • 0001407441 scopus 로고
    • The zeta functions of Ruelle and Selberg. I
    • D. FRIED, The zeta functions of Ruelle and Selberg. I, Ann. Sci. Ec. Norm. Super., IV. Ser. 19 (1986), 491-517.
    • (1986) Ann. Sci. Ec. Norm. Super., IV. Ser. , vol.19 , pp. 491-517
    • Fried, D.1
  • 11
    • 0000069887 scopus 로고
    • A Mourre estimate and related bounds for hyperbolic manifolds with cusps of non-maximal rank
    • R. FROESE, P. HISLOP, AND P. PERRY, A Mourre estimate and related bounds for hyperbolic manifolds with cusps of non-maximal rank, J. Funct. Anal. 98 (1991), 292-310.
    • (1991) J. Funct. Anal. , vol.98 , pp. 292-310
    • Froese, R.1    Hislop, P.2    Perry, P.3
  • 12
    • 0040557607 scopus 로고
    • The Laplace operator on hyperbolic three manifolds with cusps of non-maximal rank
    • _, The Laplace operator on hyperbolic three manifolds with cusps of non-maximal rank, Invent. math. 106 (1991), 295-333.
    • (1991) Invent. Math. , vol.106 , pp. 295-333
  • 13
    • 0003301335 scopus 로고
    • Introduction to the theory of linear nonselfadjoint operators
    • A.M.S., Providence
    • I. C. GOHBERG AND M. G. KREIN, Introduction to the Theory of Linear Nonselfadjoint 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
  • 14
    • 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 (1971), 603-624.
    • (1971) Math. USSR Sbornik , vol.13 , pp. 603-624
    • Gohberg, I.C.1    Sigal, E.I.2
  • 15
    • 84936178645 scopus 로고
    • Sur la distribution des longueurs des géodésiques fermées d'une surface compacte à bord totalement géodésique
    • L. GUILLOPÉ, Sur la distribution des longueurs des géodésiques fermées d'une surface compacte à bord totalement géodésique, Duke Math. J. 53 (1986), 827-848.
    • (1986) Duke Math. J. , vol.53 , pp. 827-848
    • Guillopé, L.1
  • 16
    • 0000567144 scopus 로고
    • Théorie spectrale de quelques variétés à bouts
    • _, Théorie spectrale de quelques variétés à bouts, Ann. Sci. École Norm. Sup. 22 (1989), 137-160.
    • (1989) Ann. Sci. École Norm. Sup. , vol.22 , pp. 137-160
  • 17
    • 0002814614 scopus 로고
    • Fonctions zêta de Selberg et surfaces de géométrie finie
    • _, Fonctions zêta de Selberg et surfaces de géométrie finie, Adv. Stud. Pure Math. 21 (1992), 33-70.
    • (1992) Adv. Stud. Pure Math. , vol.21 , pp. 33-70
  • 18
    • 0001081330 scopus 로고
    • Upper bounds on the number of resonances for noncompact Riemann surfaces
    • L. GUILLOPE AND M. ZWORSKI, Upper bounds on the number of resonances for noncompact Riemann surfaces, J. Funct. Anal. 129 (1995), 364-389.
    • (1995) J. Funct. Anal. , vol.129 , pp. 364-389
    • Guillope, L.1    Zworski, M.2
  • 19
    • 77950036040 scopus 로고
    • Polynomial bounds on the number of resonances for some complete spaces of constant negative curvature near infinity
    • _, Polynomial bounds on the number of resonances for some complete spaces of constant negative curvature near infinity, Asymp. Anal. 11 (1995), 1-22.
    • (1995) Asymp. Anal. , vol.11 , pp. 1-22
  • 22
    • 0002661764 scopus 로고
    • On the second term in the spectral asymptotics for Laplace-Beltrami operator on a manifold with boundary
    • V. JA. IVRII, On the second term in the spectral asymptotics for Laplace-Beltrami operator on a manifold with boundary, Funct. Anal. Appl. 14 (1980), 98-106.
    • (1980) Funct. Anal. Appl. , vol.14 , pp. 98-106
    • Ivrii, V.Ja.1
  • 23
    • 84972568716 scopus 로고
    • Spectral properties of Schrödinger operators and time-decay of the wave functions
    • A. JENSEN AND T. KATO, Spectral properties of Schrödinger operators and time-decay of the wave functions, Duke Math. J. 46 (1979), 583-610.
    • (1979) Duke Math. J. , vol.46 , pp. 583-610
    • Jensen, A.1    Kato, T.2
  • 24
    • 0000736303 scopus 로고
    • Generic simplicity of resonances
    • F. KLOPP AND M. ZWORSKI, Generic simplicity of resonances, Helv. Phys. Acta 68 (1995), 531-538.
    • (1995) Helv. Phys. Acta , vol.68 , pp. 531-538
    • Klopp, F.1    Zworski, M.2
  • 25
    • 84981750443 scopus 로고
    • Decaying modes for the wave equation in the exterior of an obstacle
    • P. LAX AND R. PHILLIPS, Decaying modes for the wave equation in the exterior of an obstacle, Comm. Pure Appl. Math. 22 (1969), 737-787.
    • (1969) Comm. Pure Appl. Math. , vol.22 , pp. 737-787
    • Lax, P.1    Phillips, R.2
  • 26
    • 84980134482 scopus 로고
    • Translation representation for the solutions of non-Euclidean wave equation I
    • _, Translation representation for the solutions of non-Euclidean wave equation I, Comm. Pure Appl. Math. 32 (1979), 617-667; II, Comm. Pure App. Math. 34 (1981), 347-358.
    • (1979) Comm. Pure Appl. Math. , vol.32 , pp. 617-667
  • 27
    • 84980130280 scopus 로고
    • Translation representation for the solutions of non-Euclidean wave equation II
    • _, Translation representation for the solutions of non-Euclidean wave equation I, Comm. Pure Appl. Math. 32 (1979), 617-667; II, Comm. Pure App. Math. 34 (1981), 347-358.
    • (1981) Comm. Pure App. Math. , vol.34 , pp. 347-358
  • 28
    • 33747199270 scopus 로고
    • The time delay operator and a related trace formula
    • Topics in Functional Analysis
    • _, The time delay operator and a related trace formula, in Topics in Functional Analysis, Adv. in Math. Suppl. Studies 3 (1978), 197-295.
    • (1978) Adv. in Math. Suppl. Studies , vol.3 , pp. 197-295
  • 29
    • 0039372210 scopus 로고
    • On the asymptotic behaviour of the spectral function and discrete spectrum of the Laplace operator on a fundamental domain of Lobachevsky's plane
    • B. M. LEVITAN, On the asymptotic behaviour of the spectral function and discrete spectrum of the Laplace operator on a fundamental domain of Lobachevsky's plane, Rend. Semin. Matem. e Fisico di Milano 52(1982), 195-219.
    • (1982) Rend. Semin. Matem. e Fisico di Milano , vol.52 , pp. 195-219
    • Levitan, B.M.1
  • 30
    • 84974253238 scopus 로고
    • Scattering operator and Eisenstein integral for kleinian groups
    • N. MANDOUVALOS, Scattering operator and Eisenstein integral for kleinian groups, Math. Proc. Cambridge Philos. Soc. 108 (1990), 203-217.
    • (1990) Math. Proc. Cambridge Philos. Soc. , vol.108 , pp. 203-217
    • Mandouvalos, N.1
  • 31
    • 0001189870 scopus 로고
    • Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature
    • R. MAZZEO AND R. B. MELROSE, Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature, J. Funct. Anal. 75 (1987), 260-310.
    • (1987) J. Funct. Anal. , vol.75 , pp. 260-310
    • Mazzeo, R.1    Melrose, R.B.2
  • 32
    • 0002995578 scopus 로고
    • Scattering theory and the trace of the wave group
    • R. B. Melrose, Scattering theory and the trace of the wave group, J. Funct. Anal. 45 (1982), 429-440.
    • (1982) J. Funct. Anal. , vol.45 , pp. 429-440
    • Melrose, R.B.1
  • 33
    • 0000179312 scopus 로고
    • Polynomial bounds on the number of scattering poles
    • _, Polynomial bounds on the number of scattering poles, J. Funct. Anal. 53 (1983), 287-303.
    • (1983) J. Funct. Anal. , vol.53 , pp. 287-303
  • 34
    • 0003335314 scopus 로고
    • Polynomial bounds on the distribution of poles in scattering by an obstacle
    • Saint-Jean de Monts
    • _, Polynomial bounds on the distribution of poles in scattering by an obstacle, Journées "Equations aux Dérivées partielles", Saint-Jean de Monts, 1984.
    • (1984) Journées "Equations aux Dérivées Partielles"
  • 35
    • 0001113896 scopus 로고
    • The trace of the wave group
    • _, The trace of the wave group, Contemp. Math. 27 (1984), 127-167.
    • (1984) Contemp. Math. , vol.27 , pp. 127-167
  • 36
    • 33846685553 scopus 로고
    • Weyl asymptotics for the phase in obstacle scattering
    • _, Weyl asymptotics for the phase in obstacle scattering, Comm. Partial Diff. Eq. 13 (1988), 1431-1439.
    • (1988) Comm. Partial Diff. Eq. , vol.13 , pp. 1431-1439
  • 37
    • 0002768927 scopus 로고
    • Pseudodifferential operators, corners and singular limits
    • Kyoto, Springer-Verlag
    • _, Pseudodifferential operators, corners and singular limits, Proc. Int. Congress Math., Kyoto, Springer-Verlag, 1990, 217-234.
    • (1990) Proc. Int. Congress Math. , pp. 217-234
  • 39
    • 0003468601 scopus 로고
    • Cambridge University Press, Cambridge, New York, Melbourne
    • _, Geometric Scattering Theory, Cambridge University Press, Cambridge, New York, Melbourne, 1995.
    • (1995) Geometric Scattering Theory
  • 40
    • 0030555213 scopus 로고    scopus 로고
    • Scattering metrics and geodesic flow at infinity
    • R. B. MELROSE AND M. ZWORSKI, Scattering metrics and geodesic flow at infinity, Invent. math. 124 (1996), 389-436.
    • (1996) Invent. Math. , vol.124 , pp. 389-436
    • Melrose, R.B.1    Zworski, M.2
  • 41
    • 0000762219 scopus 로고
    • Spectral theory for Riemannian manifold with cusps and a related trace formula
    • W. MÜLLER, Spectral theory for Riemannian manifold with cusps and a related trace formula, Math. Nach. 111 (1983), 197-288.
    • (1983) Math. Nach. , vol.111 , pp. 197-288
    • Müller, W.1
  • 42
    • 0000659640 scopus 로고
    • Spectral geometry and scattering theory for certain complete surfaces of finite volume
    • _, Spectral geometry and scattering theory for certain complete surfaces of finite volume, Invent. math. 109 (1992), 265-305.
    • (1992) Invent. Math. , vol.109 , pp. 265-305
  • 43
    • 0000194155 scopus 로고
    • Spectral asymptotics of the Laplace operator on surfaces with cusps
    • L. PARNOVSKI, Spectral asymptotics of the Laplace operator on surfaces with cusps, Math. Ann. 303 (1995), 281-296.
    • (1995) Math. Ann. , vol.303 , pp. 281-296
    • Parnovski, L.1
  • 45
    • 0009104883 scopus 로고
    • The Laplacian operator on a Riemann surface, I, II, III
    • S. PATTERSON, The Laplacian operator on a Riemann surface, I, II, III, Comp. Math. 31 (1975), 83-107, 32 (1976), 71-112, and 33 (1976), 227-259.
    • (1975) Comp. Math. , vol.31 , pp. 83-107
    • Patterson, S.1
  • 46
    • 0009261060 scopus 로고
    • S. PATTERSON, The Laplacian operator on a Riemann surface, I, II, III, Comp. Math. 31 (1975), 83-107, 32 (1976), 71-112, and 33 (1976), 227-259.
    • (1976) Comp. Math. , vol.32 , pp. 71-112
  • 47
    • 0000637979 scopus 로고
    • S. PATTERSON, The Laplacian operator on a Riemann surface, I, II, III, Comp. Math. 31 (1975), 83-107, 32 (1976), 71-112, and 33 (1976), 227-259.
    • (1976) Comp. Math. , vol.33 , pp. 227-259
  • 48
    • 0005474258 scopus 로고
    • The Selberg zeta function of a Kleinian group
    • Academic Press, Boston
    • _, The Selberg zeta function of a Kleinian group, in: Number Theory, Trace Formulas and Discrete Group, 409-441, Academic Press, Boston, 1989.
    • (1989) Number Theory, Trace Formulas and Discrete Group , pp. 409-441
  • 50
    • 38249035778 scopus 로고
    • The Laplace operator on a hyperbolic manifold: I spectral and scattering theory
    • P. PERRY, The Laplace operator on a hyperbolic manifold: I spectral and scattering theory, J. Funct. Anal. 75 (1987), 161-187.
    • (1987) J. Funct. Anal. , vol.75 , pp. 161-187
    • Perry, P.1
  • 51
    • 0005494461 scopus 로고
    • The Selberg zeta function and a local trace formula for Kleinian groups
    • _, The Selberg zeta function and a local trace formula for Kleinian groups. J. reine angew. Math. 410 (1990), 116-152.
    • (1990) J. Reine Angew. Math. , vol.410 , pp. 116-152
  • 52
    • 84968510858 scopus 로고
    • Perturbation theory for the Laplacian and automorphic forms
    • R. PHILLIPS AND P. SARNAK, Perturbation theory for the Laplacian and automorphic forms. J. A.M.S. 5 (1990), 1-32.
    • (1990) J. A.M.S. , vol.5 , pp. 1-32
    • Phillips, R.1    Sarnak, P.2
  • 53
    • 0001890705 scopus 로고
    • Sur la formule de Weyl pour des ouverts non bornés
    • D. ROBERT, Sur la formule de Weyl pour des ouverts non bornés, C. R. A. S. Série I, 319 (1994), 29-34.
    • (1994) C. R. A. S. Série I , vol.319 , pp. 29-34
    • Robert, D.1
  • 54
    • 0001085798 scopus 로고
    • Zeta functions for expanding maps and Anosov flows
    • D. RUELLE, Zeta functions for expanding maps and Anosov flows, Invent. math. 34 (1976), 231-242.
    • (1976) Invent. Math. , vol.34 , pp. 231-242
    • Ruelle, D.1
  • 55
    • 21844500409 scopus 로고
    • Existence of resonances in three dimensions
    • A. SA BARRETO AND M. ZWORSKI, Existence of resonances in three dimensions, Comm. Math. Phys. 173(2) (1995), 401-415.
    • (1995) Comm. Math. Phys. , vol.173 , Issue.2 , pp. 401-415
    • Sa Barreto, A.1    Zworski, M.2
  • 56
    • 0002350116 scopus 로고
    • Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series
    • n. Ser.
    • A. SELBERG, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc., n. Ser., 20 (1956), 47-87.
    • (1956) J. Indian Math. Soc. , vol.20 , pp. 47-87
    • Selberg, A.1
  • 57
    • 0001638909 scopus 로고
    • Göttingen lectures
    • Springer-Verlag, Berlin
    • _, Göttingen lectures, in: Collected Works. Vol. I, 626-674, Springer-Verlag, Berlin, 1989.
    • (1989) Collected Works , vol.1 , pp. 626-674
  • 58
    • 84974003886 scopus 로고
    • Geometric bounds on the density of resonances for semiclassical problems
    • J. SJÖSTRAND, Geometric bounds on the density of resonances for semiclassical problems, Duke Math. J. 60 (1990), 1-57.
    • (1990) Duke Math. J. , vol.60 , pp. 1-57
    • Sjöstrand, J.1
  • 59
    • 84968505435 scopus 로고
    • Complex scaling and the distribution of scattering poles
    • J. SJÖSTRAND AND M. ZWORSKI, Complex scaling and the distribution of scattering poles, J. A.M.S. 4 (1991), 729-769.
    • (1991) J. A.M.S. , vol.4 , pp. 729-769
    • Sjöstrand, J.1    Zworski, M.2
  • 60
    • 0001588103 scopus 로고
    • Distribution of scattering poles near the real axis
    • _, Distribution of scattering poles near the real axis, Comm. Partial Diff. Eq. 17 (1992), 1021-1035.
    • (1992) Comm. Partial Diff. Eq. , vol.17 , pp. 1021-1035
  • 61
    • 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. Partial Diff. Eq. 18 (1993), 847-857.
    • (1993) Comm. Partial Diff. Eq. , vol.18 , pp. 847-857
    • Sjöstrand, J.1    Zworski, M.2
  • 62
    • 0001031066 scopus 로고
    • Lower bounds on the number of scattering poles II
    • _, Lower bounds on the number of scattering poles II, J. Funct. Anal. 123 (1994), 336-367.
    • (1994) J. Funct. Anal. , vol.123 , pp. 336-367
  • 63
    • 0003311415 scopus 로고
    • Noncommutative harmonic analysis
    • A.M.S., Providence RI
    • M. TAYLOR, Noncommutative Harmonic Analysis, Math. Surveys and Monographs 22, A.M.S., Providence RI, 1986.
    • (1986) Math. Surveys and Monographs , vol.22
    • Taylor, M.1
  • 65
    • 0002252738 scopus 로고
    • Sharp polynomial bounds on the number of scattering poles for perturbations of the Laplacian
    • G. VODEV, Sharp polynomial bounds on the number of scattering poles for perturbations of the Laplacian, Comm. Math. Phys. 146 (1992), 39-49.
    • (1992) Comm. Math. Phys. , vol.146 , pp. 39-49
    • Vodev, G.1
  • 66
    • 0030585672 scopus 로고    scopus 로고
    • Asymptotics on the number of scattering poles for degenerate perturbations of the Laplacian
    • _, Asymptotics on the number of scattering poles for degenerate perturbations of the Laplacian, J. Func. Anal. 138 (1996), 295-310.
    • (1996) J. Func. Anal. , vol.138 , pp. 295-310
  • 67
    • 0000058086 scopus 로고
    • Kuznecov sum formulae and Szegö limit formulae on manifolds
    • S. ZELDITCH, Kuznecov sum formulae and Szegö limit formulae on manifolds. Comm. Partial Diff. Eq. 17 (1992), 221-260.
    • (1992) Comm. Partial Diff. Eq. , vol.17 , pp. 221-260
    • Zelditch, S.1
  • 68
    • 38249034950 scopus 로고
    • Distribution of poles for scattering on the real line
    • M. ZWORSKI, Distribution of poles for scattering on the real line, J. Funct. Anal. 73 (1987), 277-296.
    • (1987) J. Funct. Anal. , vol.73 , pp. 277-296
    • Zworski, M.1
  • 69
    • 84972578157 scopus 로고
    • Sharp polynomial bounds on the number of scattering poles
    • _. Sharp polynomial bounds on the number of scattering poles, Duke Math. J. 59 (1989), 311-323.
    • (1989) Duke Math. J. , vol.59 , pp. 311-323
  • 70
    • 0000548827 scopus 로고
    • Sharp polynomial bounds on the number of scattering poles of radial potentials
    • _, Sharp polynomial bounds on the number of scattering poles of radial potentials, J. Funct. Anal. 82 (1989), 370-403.
    • (1989) J. Funct. Anal. , vol.82 , pp. 370-403


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