-
1
-
-
85125839714
-
Spectral deviations for the damped wave equation
-
[Anantharaman 2009] preprint, 2009. arXiv 0904.1736 [Bogomolny et al. 1997] E. B. Bogomolny, B. Georgeot, M.-J. Giannoni, and C. Schmit, (1997), MR 99c:11062
-
[Anantharaman 2009] N. Anantharaman, “Spectral deviations for the damped wave equation”, preprint, 2009. arXiv 0904.1736 [Bogomolny et al. 1997] E. B. Bogomolny, B. Georgeot, M.-J. Giannoni, and C. Schmit, “Arithmetical chaos”, Phys. Rep.291:5-6 (1997), 219-324. MR 99c:11062
-
Arithmetical chaos”, Phys. Rep
, vol.291
, Issue.5-6
, pp. 219-324
-
-
Anantharaman, N.1
-
2
-
-
49549094427
-
Spectral theory ofinfinite-area hyperbolic surfaces
-
[Borthwick 2007] Birkhäuser, Boston,MA,. MR2008h:58056 Zbl 1130.58001
-
[Borthwick 2007] D. Borthwick, Spectral theory ofinfinite-area hyperbolic surfaces, Progress in Mathematics 256, Birkhäuser, Boston,MA,2007. MR2008h:58056 Zbl 1130.58001
-
(2007)
Progress in Mathematics
, vol.256
-
-
Borthwick, D.1
-
3
-
-
49549084186
-
Upper and lower bounds on resonances for manifolds hyperbolic near infinity
-
[Borthwick 2008] MR 2009i:58039 Zbl 1168.58012
-
[Borthwick 2008] D. Borthwick, “Upper and lower bounds on resonances for manifolds hyperbolic near infinity”, Comm. PartialDifferentialEquations 33:7-9 (2008), 1507-1539. MR 2009i:58039 Zbl 1168.58012
-
(2008)
Comm. PartialDifferentialEquations
, vol.33
, Issue.7-9
, pp. 1507-1539
-
-
Borthwick, D.1
-
5
-
-
0142168845
-
On the spectral gap for infinite index “congruence” subgroups of SL2(Z)
-
[Gamburd 2002] MR2003b:11050
-
[Gamburd 2002] A. Gamburd, “On the spectral gap for infinite index “congruence” subgroups of SL2(Z)”, Israel J. Math. 127 (2002), 157-200. MR2003b:11050
-
(2002)
Israel J. Math
, vol.127
, pp. 157-200
-
-
Gamburd, A.1
-
6
-
-
33846651297
-
Wave 0-trace and length spectrum on convex co-compact hyperbolic manifolds
-
[Guillarmou and Naud 2006] MR 2008f:58032 Zbl 1127.58028
-
[Guillarmou and Naud 2006] C. Guillarmou and F. Naud, “Wave 0-trace and length spectrum on convex co-compact hyperbolic manifolds”, Comm. Anal. Geom. 14:5 (2006), 945-967. MR 2008f:58032 Zbl 1127.58028
-
(2006)
Comm. Anal. Geom
, vol.14
, Issue.5
, pp. 945-967
-
-
Guillarmou, C.1
Naud, F.2
-
7
-
-
0001081330
-
Upper bounds on the number of resonances for non-compact Riemann surfaces
-
[Guillopé and Zworski 1995] MR 96b:58116 Zbl 0841.58063
-
[Guillopé and Zworski 1995] L. Guillopé and M. Zworski, “Upper bounds on the number of resonances for non-compact Riemann surfaces”, J. Funct. Anal. 129:2 (1995), 364-389. MR 96b:58116 Zbl 0841.58063
-
(1995)
J. Funct. Anal
, vol.129
, Issue.2
, pp. 364-389
-
-
Guillopé, L.1
Zworski, M.2
-
8
-
-
0031486229
-
Scattering asymptotics for Riemann surfaces
-
[Guillopé and Zworski 1997] MR98g:58181 Zbl0898.58054
-
[Guillopé and Zworski 1997] L. Guillopé and M. Zworski, “Scattering asymptotics for Riemann surfaces”, Ann. of Math. (2) 145:3 (1997),597-660. MR98g:58181 Zbl0898.58054
-
(1997)
Ann. of Math. (2)
, vol.145
, Issue.3
, pp. 597-660
-
-
Guillopé, L.1
Zworski, M.2
-
9
-
-
0033276488
-
The wave trace for Riemann surfaces
-
[Guillopé and Zworski 1999] MR2001a:11086 Zbl0947.58022
-
[Guillopé and Zworski 1999] L. Guillopé and M. Zworski, “The wave trace for Riemann surfaces”, Geom. Funct. Anal. 9:6 (1999),1156-1168. MR2001a:11086 Zbl0947.58022
-
(1999)
Geom. Funct. Anal
, vol.9
, Issue.6
, pp. 1156-1168
-
-
Guillopé, L.1
Zworski, M.2
-
10
-
-
1542403824
-
The Selberg zeta function for convex co-compact Schottky groups
-
[Guillopé et al. 2004] MR 2005f:11193 Zbl 1075.11059
-
[Guillopé et al. 2004] L. Guillopé, K. K. Lin, and M. Zworski, “The Selberg zeta function for convex co-compact Schottky groups”, Comm. Math. Phys. 245:1 (2004), 149-176. MR 2005f:11193 Zbl 1075.11059
-
(2004)
Comm. Math. Phys
, vol.245
, Issue.1
, pp. 149-176
-
-
Guillopé, L.1
Lin, K. K.2
Zworski, M.3
-
11
-
-
0003586158
-
-
[Hejhal 1976] Springer, Berlin, MR55#12641 Zbl0347.10018
-
[Hejhal 1976] D. A. Hejhal, The Selberg traceformulafor PSL(2, R), I, Lecture Notes in Math. 548, Springer, Berlin, 1976. MR55#12641 Zbl0347.10018
-
(1976)
The Selberg traceformulafor PSL(2, R), I, Lecture Notes in Math
, vol.548
-
-
Hejhal, D. A.1
-
12
-
-
35148850933
-
Estimates from below for the spectral function and for the remainder in localWeyl’s law
-
[Jakobson and Polterovich 2007] MR 2009h:35302 Zbl 1161.58012
-
[Jakobson and Polterovich 2007] D. Jakobson and I. Polterovich, “Estimates from below for the spectral function and for the remainder in localWeyl’s law”, Geom. Funct. Anal. 17:3 (2007), 806-838. MR 2009h:35302 Zbl 1161.58012
-
(2007)
Geom. Funct. Anal
, vol.17
, Issue.3
, pp. 806-838
-
-
Jakobson, D.1
Polterovich, I.2
-
13
-
-
84904331560
-
A lower bound for the remainder in Weyl’s law on negatively curved surfaces
-
[Jakobson et al. 2008] MR 2009f:58038
-
[Jakobson et al. 2008] D. Jakobson, I. Polterovich, and J. A. Toth, “A lower bound for the remainder in Weyl’s law on negatively curved surfaces”, Int. Math. Res. Not. 2008:2 (2008). MR 2009f:58038
-
(2008)
Int. Math. Res. Not
, vol.2008
, pp. 2
-
-
Jakobson, D.1
Polterovich, I.2
Toth, J. A.3
-
14
-
-
0004117363
-
-
[Katok 1992] University ofChicago Press, Chicago, MR 93d:20088 Zbl 0753.30001
-
[Katok 1992] S. Katok, Fuchsian groups, University ofChicago Press, Chicago, 1992. MR 93d:20088 Zbl 0753.30001
-
(1992)
Fuchsian groups
-
-
Katok, S.1
-
15
-
-
84990600904
-
Translation representation for automorphic solutions of the wave equation in non-Euclidean spaces, I
-
[Lax and Phillips 1984a] MR 86c:58148 Zbl 0549.10024
-
[Lax and Phillips 1984a] P. D. Lax and R. S. Phillips, “Translation representation for automorphic solutions of the wave equation in non-Euclidean spaces, I”, Comm. Pure Appl. Math. 37:3 (1984), 303-328. MR 86c:58148 Zbl 0549.10024
-
(1984)
Comm. Pure Appl. Math
, vol.37
, Issue.3
, pp. 303-328
-
-
Lax, P. D.1
Phillips, R. S.2
-
16
-
-
84990553480
-
Translation representations for automorphic solutions of the wave equation in non-Euclidean spaces, II
-
[Lax and Phillips 1984b] MR 86h:58140 Zbl 0549.10019
-
[Lax and Phillips 1984b] P. D. Lax and R. S. Phillips, “Translation representations for automorphic solutions of the wave equation in non-Euclidean spaces, II”, Comm. PureAppl. Math. 37:6 (1984), 779-813. MR 86h:58140 Zbl 0549.10019
-
(1984)
Comm. PureAppl. Math
, vol.37
, Issue.6
, pp. 779-813
-
-
Lax, P. D.1
Phillips, R. S.2
-
17
-
-
84990578234
-
Translation representations for automorphic solutions of the wave equation in non-Euclidean spaces, III
-
[Lax and Phillips 1985] MR 86j:58150 Zbl 0578.10033
-
[Lax and Phillips 1985] P. D. Lax and R. S. Phillips, “Translation representations for automorphic solutions of the wave equation in non-Euclidean spaces, III”, Comm. PureAppl. Math. 38:2 (1985), 179-207. MR 86j:58150 Zbl 0578.10033
-
(1985)
Comm. PureAppl. Math
, vol.38
, Issue.2
, pp. 179-207
-
-
Lax, P. D.1
Phillips, R. S.2
-
18
-
-
21344479357
-
Number variance for arithmetic hyperbolic surfaces
-
[Luo and Sarnak 1994] MR95k:11076 Zbl0797.58069
-
[Luo and Sarnak 1994] W. Luo and P. Sarnak, “Number variance for arithmetic hyperbolic surfaces”, Comm. Math. Phys. 161:2 (1994),419-432. MR95k:11076 Zbl0797.58069
-
(1994)
Comm. Math. Phys
, vol.161
, Issue.2
, pp. 419-432
-
-
Luo, W.1
Sarnak, P.2
-
19
-
-
0001189870
-
Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature
-
[Mazzeo and Melrose 1987] MR 89c:58133 Zbl 0636.58034
-
[Mazzeo and Melrose 1987] R. R. Mazzeo and R. B. Melrose, “Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature”, J. Funct. Anal. 75:2 (1987), 260-310. MR 89c:58133 Zbl 0636.58034
-
(1987)
J. Funct. Anal
, vol.75
, Issue.2
, pp. 260-310
-
-
Mazzeo, R. R.1
Melrose, R. B.2
-
20
-
-
16244383902
-
Precise asymptotics of the length spectrum for finite-geometry Riemann surfaces
-
[Naud 2005] Zbl 1073.37021
-
[Naud 2005] F. Naud, “Precise asymptotics of the length spectrum for finite-geometry Riemann surfaces”, Int. Math. Res. Not. 2005 (2005), 299-310. Zbl 1073.37021
-
(2005)
Int. Math. Res. Not
, vol.2005
, pp. 299-310
-
-
Naud, F.1
-
21
-
-
0000131067
-
The limit set of a Fuchsian group
-
[Patterson 1976] MR 56 #8841 Zbl 0336.30005
-
[Patterson 1976] S. J. Patterson, “The limit set of a Fuchsian group”, Acta Math. 136:3-4 (1976), 241-273. MR 56 #8841 Zbl 0336.30005
-
(1976)
Acta Math
, vol.136
, Issue.3-4
, pp. 241-273
-
-
Patterson, S. J.1
-
22
-
-
84972558528
-
On the spectrum of the Hecke groups
-
[Phillips and Sarnak 1985] MR86j:11042 Zbl0564.30030
-
[Phillips and Sarnak 1985] R. S. Phillips and P. Sarnak, “On the spectrum of the Hecke groups”, Duke Math. J. 52:1 (1985), 211-221. MR86j:11042 Zbl0564.30030
-
(1985)
Duke Math. J
, vol.52
, Issue.1
, pp. 211-221
-
-
Phillips, R. S.1
Sarnak, P.2
-
23
-
-
0013099996
-
Ground state and lowest eigenvalue of the Laplacian for noncompact hyperbolic surfaces
-
[Pignataro and Sullivan 1986] MR 87m:58178
-
[Pignataro and Sullivan 1986] T. Pignataro and D. Sullivan, “Ground state and lowest eigenvalue of the Laplacian for noncompact hyperbolic surfaces”, Comm. Math. Phys. 104:4 (1986), 529-535. MR 87m:58178
-
(1986)
Comm. Math. Phys
, vol.104
, Issue.4
, pp. 529-535
-
-
Pignataro, T.1
Sullivan, D.2
-
24
-
-
84974003886
-
Geometric bounds on the density of resonances for semiclassical problems
-
[Sjostrand 1990] MR91e:35166 Zbl0702.35188
-
[Sjostrand 1990] J. Sjostrand, “Geometric bounds on the density of resonances for semiclassical problems”, Duke Math. J. 60:1 (1990), 1-57. MR91e:35166 Zbl0702.35188
-
(1990)
Duke Math. J
, vol.60
, Issue.1
, pp. 1-57
-
-
Sjostrand, J.1
-
25
-
-
34248399658
-
Fractal upper bounds on the density of semiclassical resonances
-
[Sjostrand and Zworski 2007] MR2008e:35037 Zbl05154881
-
[Sjostrand and Zworski 2007] J. Sjostrand and M. Zworski, “Fractal upper bounds on the density of semiclassical resonances”, DukeMath.J.137:3 (2007),381-459. MR2008e:35037 Zbl05154881
-
(2007)
DukeMath.J
, vol.137
, Issue.3
, pp. 381-459
-
-
Sjostrand, J.1
Zworski, M.2
-
26
-
-
51249182653
-
The density at infinity of a discrete group of hyperbolic motions
-
[Sullivan 1979] MR81b:58031 Zbl0439.30034
-
[Sullivan 1979] D. Sullivan, “The density at infinity of a discrete group of hyperbolic motions”, Inst. Hautes Études Sci. Publ. Math. 50 (1979),171-202. MR81b:58031 Zbl0439.30034
-
(1979)
Inst. Hautes Études Sci. Publ. Math
, vol.50
, pp. 171-202
-
-
Sullivan, D.1
-
27
-
-
0000144097
-
Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups
-
[Sullivan 1984] MR86c:58093 Zbl0566.58022
-
[Sullivan 1984] D. Sullivan, “Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups”, ActaMath. 153:3-4(1984),259-277. MR86c:58093 Zbl0566.58022
-
(1984)
ActaMath
, vol.153
, Issue.3-4
, pp. 259-277
-
-
Sullivan, D.1
-
28
-
-
84972494106
-
A characterization of arithmetic Fuchsian groups
-
[Takeuchi 1975] MR53#2842 Zbl0311.20030
-
[Takeuchi 1975] K. Takeuchi, “A characterization of arithmetic Fuchsian groups”, J. Math. Soc. Japan 27:4 (1975), 600-612.MR53#2842 Zbl0311.20030
-
(1975)
J. Math. Soc. Japan
, vol.27
, Issue.4
, pp. 600-612
-
-
Takeuchi, K.1
-
29
-
-
0033473946
-
Dimension of the limit set and the density of resonances for convex co-compact hyperbolic surfaces
-
[Zworski 1999] MR 2002d:58038 Zbl 1016.58014
-
[Zworski 1999] M. Zworski, “Dimension of the limit set and the density of resonances for convex co-compact hyperbolic surfaces”, Invent.Math. 136:2(1999),353-409. MR 2002d:58038 Zbl 1016.58014
-
(1999)
Invent.Math
, vol.136
, Issue.2
, pp. 353-409
-
-
Zworski, M.1
|