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Volumn 172, Issue 1, 2000, Pages 76-164

The Spectrum of Kleinian Manifolds

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EID: 0041993862     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1999.3494     Document Type: Article
Times cited : (23)

References (58)
  • 1
    • 84990604696 scopus 로고
    • Spectral theory of Schrödinger operators on Euclidean and non-Euclidean spaces
    • Agmon S. 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 , pp. 3-S16
    • Agmon, S.1
  • 3
    • 84972577239 scopus 로고
    • The unitary dual of Sp(n, 1), n≥2
    • Baldoni Silva M. W. The unitary dual of Sp(n, 1), n≥2. Duke Math. J. 48:1991;549-583.
    • (1991) Duke Math. J. , vol.48 , pp. 549-583
    • Baldoni Silva, M.W.1
  • 4
    • 0039426944 scopus 로고
    • The unitary spectrum for real rank one groups
    • Baldoni Silva M. W., Barbasch D. The unitary spectrum for real rank one groups. Invent. Math. 72:1983;27-55.
    • (1983) Invent. Math. , vol.72 , pp. 27-55
    • Baldoni Silva, M.W.1    Barbasch, D.2
  • 5
    • 0001359223 scopus 로고
    • The principal series for a reductive symmetric space
    • van den Ban E. P. The principal series for a reductive symmetric space. Ann. scient. Éc. Norm. Sup. 21:1988;359-412.
    • (1988) Ann. Scient. Éc. Norm. Sup. , vol.21 , pp. 359-412
    • Van Den Ban, E.P.1
  • 6
    • 0001597577 scopus 로고
    • Local boundary data of eigenfunctions on a Riemannian symmetric space
    • van den Ban E. P., Schlichtkrull H. Local boundary data of eigenfunctions on a Riemannian symmetric space. Invent. Math. 98:1989;639-657.
    • (1989) Invent. Math. , vol.98 , pp. 639-657
    • Van Den Ban, E.P.1    Schlichtkrull, H.2
  • 7
    • 0031505891 scopus 로고    scopus 로고
    • Fourier transforms on a semisimple symmetric space
    • van den Ban E. P., Schlichtkrull H. Fourier transforms on a semisimple symmetric space. Invent. Math. 130:1997;517-574.
    • (1997) Invent. Math. , vol.130 , pp. 517-574
    • Van Den Ban, E.P.1    Schlichtkrull, H.2
  • 8
    • 0000649145 scopus 로고
    • On the support of the Plancherel measure
    • Bernstein J. N. On the support of the Plancherel measure. J. of Geom. and Phys. 5:1988;663-710.
    • (1988) J. of Geom. and Phys. , vol.5 , pp. 663-710
    • Bernstein, J.N.1
  • 9
    • 0001514920 scopus 로고
    • Vecteurs distributions H-invariants pour les séries principales généralisées d'espaces symétriques réductifs et prolongement méromorphe d'intégrales d'Eisenstein
    • Brylinski J. L., Delorme P. Vecteurs distributions H-invariants pour les séries principales généralisées d'espaces symétriques réductifs et prolongement méromorphe d'intégrales d'Eisenstein. Invent. Math. 109:1992;619-664.
    • (1992) Invent. Math. , vol.109 , pp. 619-664
    • Brylinski, J.L.1    Delorme, P.2
  • 10
    • 0000689606 scopus 로고
    • Gamma-cohomology and the Selberg zeta function
    • Bunke U., Olbrich M. Gamma-cohomology and the Selberg zeta function. J. Reine Angew. Math. 467:1995;199-219.
    • (1995) J. Reine Angew. Math. , vol.467 , pp. 199-219
    • Bunke, U.1    Olbrich, M.2
  • 12
    • 0032222344 scopus 로고    scopus 로고
    • Resolutions of distribution globalizations of Harish-Chandra modules and cohomology
    • Bunke U., Olbrich M. Resolutions of distribution globalizations of Harish-Chandra modules and cohomology. J. Reine Angew. Math. 497:1998;47-81.
    • (1998) J. Reine Angew. Math. , vol.497 , pp. 47-81
    • Bunke, U.1    Olbrich, M.2
  • 13
    • 0033422076 scopus 로고    scopus 로고
    • Group cohomology and the singularities of the Selberg zeta function associated to a Kleinian group
    • Bunke U., Olbrich M. Group cohomology and the singularities of the Selberg zeta function associated to a Kleinian group. Ann. of Math. 149:1999;627-689.
    • (1999) Ann. of Math. , vol.149 , pp. 627-689
    • Bunke, U.1    Olbrich, M.2
  • 14
    • 0001194302 scopus 로고
    • Base méromorphe de vecteurs distributions H-invariants pour les séries principales généralisées d'espaces symétriques réductifs. Equations fonctionelle
    • Carmona J., Delorme P. Base méromorphe de vecteurs distributions H-invariants pour les séries principales généralisées d'espaces symétriques réductifs. Equations fonctionelle. J. Funct. Anal. 122:1994;152-221.
    • (1994) J. Funct. Anal. , vol.122 , pp. 152-221
    • Carmona, J.1    Delorme, P.2
  • 15
    • 0001291539 scopus 로고
    • Canonical extensions of Harish-Chandra modules
    • Casselman W. Canonical extensions of Harish-Chandra modules. Canadian J. Math. 41:1989;385-438.
    • (1989) Canadian J. Math. , vol.41 , pp. 385-438
    • Casselman, W.1
  • 16
    • 0041151698 scopus 로고
    • Théorie spectrale et surfaces de Riemann d'aire infinie
    • Colin de Verdière Y. Théorie spectrale et surfaces de Riemann d'aire infinie. Astérisque. 132:1985;259-275.
    • (1985) Astérisque , vol.132 , pp. 259-275
    • Colin De Verdière, Y.1
  • 17
    • 0042303965 scopus 로고
    • Representations of Rank One Lie Groups
    • Boston: Pitman
    • Collingwood D. H. Representations of Rank One Lie Groups. Research Notes in Math. 137:1985;Pitman, Boston.
    • (1985) Research Notes in Math. , vol.137
    • Collingwood, D.H.1
  • 18
    • 0000138280 scopus 로고
    • Hausdorff dimensions of limit sets
    • Corlette K. Hausdorff dimensions of limit sets. Invent. Math. 102:1990;521-542.
    • (1990) Invent. Math. , vol.102 , pp. 521-542
    • Corlette, K.1
  • 19
    • 0032364138 scopus 로고    scopus 로고
    • Formule de Plancherel pour les espaces symétriques réductifs
    • Delorme P. Formule de Plancherel pour les espaces symétriques réductifs. Ann. of Math. 147:1998;417-452.
    • (1998) Ann. of Math. , vol.147 , pp. 417-452
    • Delorme, P.1
  • 20
    • 0012889467 scopus 로고
    • Die Resolvente zum Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene III
    • Elstrodt J. Die Resolvente zum Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene III. Math. Annalen. 208:1975;99-132.
    • (1975) Math. Annalen , vol.208 , pp. 99-132
    • Elstrodt, J.1
  • 22
    • 33746647876 scopus 로고
    • Resolvent of the Laplacian on strictly pseudoconvex domains
    • Epstein C. L., Melrose R. B., Mendoza G. A. Resolvent of the Laplacian on strictly pseudoconvex domains. Acta Math. 167:1991;1-106.
    • (1991) Acta Math. , vol.167 , pp. 1-106
    • Epstein, C.L.1    Melrose, R.B.2    Mendoza, G.A.3
  • 23
    • 84941432866 scopus 로고
    • Fourier coefficients of the resolvent for a Fuchsian group
    • Fay J. D. Fourier coefficients of the resolvent for a Fuchsian group. J. Reine Angew. Math. 293:1977;143-203.
    • (1977) J. Reine Angew. Math. , vol.293 , pp. 143-203
    • Fay, J.D.1
  • 24
    • 0000069887 scopus 로고
    • A Mourre estimate and related bounds for hyperbolic manifolds with cusps of non-maximal rank
    • Froese R., Hislop P., Perry P. 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
  • 25
    • 0010748025 scopus 로고
    • Two theorems on semisimple Lie groups
    • Harish-Chandra. Two theorems on semisimple Lie groups. Ann. of Math. 83:1966;74-128.
    • (1966) Ann. of Math. , vol.83 , pp. 74-128
    • Harish-Chandra1
  • 26
    • 0001614669 scopus 로고
    • Harmonic analysis on real reductive groups III. The Maass-Selberg relations and the Plancherel formula
    • Harish-Chandra. Harmonic analysis on real reductive groups III. The Maass-Selberg relations and the Plancherel formula. Ann. of Math. 104:1976;117-201.
    • (1976) Ann. of Math. , vol.104 , pp. 117-201
    • Harish-Chandra1
  • 29
    • 0002021591 scopus 로고
    • Geometric Analysis on Symmetric Spaces
    • Providence: Amer. Mah. Soc.
    • Helgason S. Geometric Analysis on Symmetric Spaces. Math. Surveys. 39:1994;Amer. Mah. Soc. Providence.
    • (1994) Math. Surveys , vol.39
    • Helgason, S.1
  • 30
    • 0009085075 scopus 로고
    • The Plancherel formula of the Lorentz group of n'th order
    • Hirai T. The Plancherel formula of the Lorentz group of n'th order. Proc. Japan Acad. 42:1966;323-326.
    • (1966) Proc. Japan Acad. , vol.42 , pp. 323-326
    • Hirai, T.1
  • 32
    • 0000651893 scopus 로고
    • Intertwining operators for semisimple Lie groups
    • Knapp A. W., Stein E. M. Intertwining operators for semisimple Lie groups. Ann. of Math. 93:1971;489-578.
    • (1971) Ann. of Math. , vol.93 , pp. 489-578
    • Knapp, A.W.1    Stein, E.M.2
  • 33
    • 0000671679 scopus 로고
    • The asymptotic distribution of lattice points in Euclidian and non-Euclidian spaces
    • Lax P. D., Phillips R. S. The asymptotic distribution of lattice points in Euclidian and non-Euclidian spaces. J. Funct. Anal. 46:1982;280-350.
    • (1982) J. Funct. Anal. , vol.46 , pp. 280-350
    • Lax, P.D.1    Phillips, R.S.2
  • 34
    • 84990600904 scopus 로고
    • Translation representations for automorphic solutions of the wave equation in non-Euclidian spaces I/II
    • Lax P. D., Phillips R. S. Translation representations for automorphic solutions of the wave equation in non-Euclidian spaces I/II. Comm. Pure Appl. Math. 37:1984;303-328.
    • (1984) Comm. Pure Appl. Math. , vol.37 , pp. 303-328
    • Lax, P.D.1    Phillips, R.S.2
  • 35
    • 84990578234 scopus 로고
    • Translation representations for automorphic solutions of the wave equation in non-Euclidian spaces III
    • Lax P. D., Phillips R. S. Translation representations for automorphic solutions of the wave equation in non-Euclidian spaces III. Comm. Pure Appl. Math. 38:1985;197-208.
    • (1985) Comm. Pure Appl. Math. , vol.38 , pp. 197-208
    • Lax, P.D.1    Phillips, R.S.2
  • 36
    • 0039659682 scopus 로고
    • The theory of Eisenstein series for Kleinian groups
    • Mandouvalos N. The theory of Eisenstein series for Kleinian groups. Contemp. Math. 53:1986;358-370.
    • (1986) Contemp. Math. , vol.53 , pp. 358-370
    • Mandouvalos, N.1
  • 37
    • 84962994112 scopus 로고
    • Spectral theory and Eisenstein series for Kleinian groups
    • Mandouvalos N. Spectral theory and Eisenstein series for Kleinian groups. Proc. London Math. Soc. 57:1988;209-238.
    • (1988) Proc. London Math. Soc. , vol.57 , pp. 209-238
    • Mandouvalos, N.1
  • 38
    • 0039067585 scopus 로고
    • Scattering operator, Eisenstein series, inner product formula and "maass-Selberg" relations for Kleinian groups
    • Mandouvalos N. Scattering operator, Eisenstein series, inner product formula and "Maass-Selberg" relations for Kleinian groups. Mem. Amer. Math. Soc. 78:1978.
    • (1978) Mem. Amer. Math. Soc. , vol.78
    • Mandouvalos, N.1
  • 39
    • 0001189870 scopus 로고
    • Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature
    • Mazzeo R., Melrose R. 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.2
  • 40
    • 84974002892 scopus 로고
    • Hodge theory on hyperbolic manifolds
    • Mazzeo R., Phillips R. Hodge theory on hyperbolic manifolds. Duke Math. J. 60:1990;509-559.
    • (1990) Duke Math. J. , vol.60 , pp. 509-559
    • Mazzeo, R.1    Phillips, R.2
  • 41
    • 84972553721 scopus 로고
    • On the Plancherel formulas for some types of simple Lie groups
    • Okamoto K. On the Plancherel formulas for some types of simple Lie groups. Osaka J. Math. 2:1965;247-282.
    • (1965) Osaka J. Math. , vol.2 , pp. 247-282
    • Okamoto, K.1
  • 44
    • 0009104883 scopus 로고
    • The Laplace operator on a Riemann surface I
    • Patterson S. J. The Laplace operator on a Riemann surface I. Comp. Math. 31:1975;83-107.
    • (1975) Comp. Math. , vol.31 , pp. 83-107
    • Patterson, S.J.1
  • 45
    • 0009261060 scopus 로고
    • The Laplace operator on a Riemann surface II
    • Patterson S. J. The Laplace operator on a Riemann surface II. Comp. Math. 32:1976;71-112.
    • (1976) Comp. Math. , vol.32 , pp. 71-112
    • Patterson, S.J.1
  • 46
    • 0000637979 scopus 로고
    • The Laplace operator on a Riemann surface III
    • Patterson S. J. The Laplace operator on a Riemann surface III. Comp. Math. 33:1976;227-259.
    • (1976) Comp. Math. , vol.33 , pp. 227-259
    • Patterson, S.J.1
  • 47
    • 0000131067 scopus 로고
    • The limit set of a Fuchsian group
    • Patterson S. J. The limit set of a Fuchsian group. Acta Math. 136:1976;241-273.
    • (1976) Acta Math. , vol.136 , pp. 241-273
    • Patterson, S.J.1
  • 48
    • 38249035778 scopus 로고
    • The Laplace operator on a hyperbolic manifold I. Spectral and scattering theory
    • Perry P. A. 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.A.1
  • 49
    • 0003114897 scopus 로고
    • The Laplace operator on a hyperbolic manifold II. Eisenstein series and the scattering matrix
    • Perry P. A. The Laplace operator on a hyperbolic manifold II. Eisenstein series and the scattering matrix. J. Reine Angew. Math. 398:1989;67-91.
    • (1989) J. Reine Angew. Math. , vol.398 , pp. 67-91
    • Perry, P.A.1
  • 52
    • 51249182653 scopus 로고
    • The density at infinity of a discrete group of hyperbolic motions
    • Sullivan D. The density at infinity of a discrete group of hyperbolic motions. I.H.E.D. Publ. Math. 50:1979;171-209.
    • (1979) I.H.E.D. Publ. Math. , vol.50 , pp. 171-209
    • Sullivan, D.1
  • 54
    • 0009085272 scopus 로고
    • Vector valued Poisson transforms on Riemannian symmetric spaces of rank one
    • van der Ven H. Vector valued Poisson transforms on Riemannian symmetric spaces of rank one. J. Funct. Anal. 119:1994;358-400.
    • (1994) J. Funct. Anal. , vol.119 , pp. 358-400
    • Van Der Ven, H.1
  • 58
    • 21944437915 scopus 로고    scopus 로고
    • Poisson transforms on vector bundles
    • Yang An. Poisson transforms on vector bundles. Trans. Amer. Math. Soc. 350:1998;857-887.
    • (1998) Trans. Amer. Math. Soc. , vol.350 , pp. 857-887
    • Yang, A.1


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