Spectral estimates around a critical level
R. Brummelhuis, T. Paul, and A. Uribe
Source: Duke Math. J. Volume 78, Number 3
(1995), 477-530.
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Mathematical Reviews number (MathSciNet): MR1334204
Zentralblatt MATH identifier: 0849.58067
Digital Object Identifier: doi:10.1215/S0012-7094-95-07823-5
References
[1] V. I. Arnold, S. M. Gusein-Zade, and A. N. Varchenko, Singularities of differentiable maps. Vol. I, Monographs in Mathematics, vol. 82, Birkhäuser Boston Inc., Boston, MA, 1985.
Mathematical Reviews (MathSciNet): MR86f:58018
Zentralblatt MATH: 0554.58001
[2] J. Brüning and R. Seeley, Regular singular asymptotics, Adv. in Math. 58 (1985), no. 2, 133–148.
Mathematical Reviews (MathSciNet): MR87b:41032
Zentralblatt MATH: 0593.47047
Digital Object Identifier: doi:10.1016/0001-8708(85)90114-8
[3] R. Brummelhuis and A. Uribe, A semi-classical trace formula for Schrödinger operators, Comm. Math. Phys. 136 (1991), no. 3, 567–584.
Mathematical Reviews (MathSciNet): MR92c:35085
Zentralblatt MATH: 0729.35093
Digital Object Identifier: doi:10.1007/BF02099074
Project Euclid: euclid.cmp/1104202437
[4] C. J. Callias and G. A. Uhlmann, Singular asymptotics approach to partial differential equations with isolated singularities in the coefficients, Bull. Amer. Math. Soc. (N.S.) 11 (1984), no. 1, 172–176.
Mathematical Reviews (MathSciNet): MR85i:35116
Zentralblatt MATH: 0568.35074
Digital Object Identifier: doi:10.1090/S0273-0979-1984-15255-8
Project Euclid: euclid.bams/1183551843
[5] Y. Colin De Verdière, Ergodicité et fonctions propres du laplacien, Comm. Math. Phys. 102 (1985), no. 3, 497–502.
Mathematical Reviews (MathSciNet): MR87d:58145
Zentralblatt MATH: 0592.58050
Digital Object Identifier: doi:10.1007/BF01209296
Project Euclid: euclid.cmp/1104114465
[6] Y. Colin de Verdière and B. Parisse, Équilibre instable en régime semi-classique I: Concentration microlocale, preprint, 1993.
Mathematical Reviews (MathSciNet): MR1294470
Digital Object Identifier: doi:10.1080/03605309408821063
[7] P. Duclos and H. Hogreve, On the semiclassical localization of the quantum probability, J. Math. Phys. 34 (1993), no. 5, 1681–1691.
Mathematical Reviews (MathSciNet): MR94b:81028
Zentralblatt MATH: 0773.60094
Digital Object Identifier: doi:10.1063/1.530408
[8] J. Duistermaat, Fourier integral operators, Courant Institute of Mathematical Sciences New York University, New York, 1973.
Mathematical Reviews (MathSciNet): MR56:9600
Zentralblatt MATH: 0272.47028
[9] J. J. Duistermaat and V. Guillemin, The spectrum of positive elliptic operators and periodic bicharacteristics, Invent. Math. 29 (1975), no. 1, 39–79.
Mathematical Reviews (MathSciNet): MR53:9307
Zentralblatt MATH: 0307.35071
Digital Object Identifier: doi:10.1007/BF01405172
[10] B. Helffer, A. Martinez, and D. Robert, Ergodicité et limite semi-classique, Comm. Math. Phys. 109 (1987), no. 2, 313–326.
Mathematical Reviews (MathSciNet): MR88e:81029
Zentralblatt MATH: 0624.58039
Digital Object Identifier: doi:10.1007/BF01215225
Project Euclid: euclid.cmp/1104116844
[11] V. Guillemin and G. Uhlmann, Oscillatory integrals with singular symbols, Duke Math. J. 48 (1981), no. 1, 251–267.
Mathematical Reviews (MathSciNet): MR82d:58065
Zentralblatt MATH: 0462.58030
Digital Object Identifier: doi:10.1215/S0012-7094-81-04814-6
Project Euclid: euclid.dmj/1077314493
[12] V. Guillemin and A. Uribe, Circular symmetry and the trace formula, Invent. Math. 96 (1989), no. 2, 385–423.
Mathematical Reviews (MathSciNet): MR90e:58159
Zentralblatt MATH: 0686.58040
Digital Object Identifier: doi:10.1007/BF01393968
[13] S. Jones, Generalised functions, McGraw-Hill Book Co., New York, 1966.
Mathematical Reviews (MathSciNet): MR36:623
Zentralblatt MATH: 0149.09403
[14] L. Hörmander, The analysis of linear partial differential operators. I, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 256, Springer-Verlag, Berlin, 1983.
Mathematical Reviews (MathSciNet): MR85g:35002a
Zentralblatt MATH: 0521.35001
[15] L. Hörmander, The analysis of linear partial differential operators. III, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 274, Springer-Verlag, Berlin, 1985.
Mathematical Reviews (MathSciNet): MR87d:35002a
Zentralblatt MATH: 0601.35001
[16] L. Hörmander, The analysis of linear partial differential operators. IV, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 275, Springer-Verlag, Berlin, 1985.
Mathematical Reviews (MathSciNet): MR87d:35002b
Zentralblatt MATH: 0612.35001
[17] B. Malgrange, Intégrales asymptotiques et monodromie, Ann. Sci. École Norm. Sup. (4) 7 (1974), 405–430 (1975).
Mathematical Reviews (MathSciNet): MR51:8459
Zentralblatt MATH: 0305.32008
[18] R. B. Melrose and G. Uhlmann, Lagrangian intersection and the Cauchy problem, Comm. Pure Appl. Math. 32 (1979), no. 4, 483–519.
Mathematical Reviews (MathSciNet): MR81d:58052
Zentralblatt MATH: 0396.58006
Digital Object Identifier: doi:10.1002/cpa.3160320403
[19] T. Paul and A. Uribe, Sur la formule semi-classique des traces, C. R. Acad. Sci. Paris Sér. I Math. 313 (1991), no. 5, 217–222.
Mathematical Reviews (MathSciNet): MR93d:58161
Zentralblatt MATH: 0738.58046
[20] T. Paul and A. Uribe, The semi-classical trace formula and propagation of wave packets, to appear in J. Funct. Analysis.
Mathematical Reviews (MathSciNet): MR1346223
Zentralblatt MATH: 0837.35106
Digital Object Identifier: doi:10.1006/jfan.1995.1105
[21] T. Paul and A. Uribe, Periodic orbits and quantum mechanics, From Classical to Quantum Chaos eds. G. F. Dell'Antonio, S. Fantoni and V. R. Manfredi, Società Italiana di Fisica, Bologna, 1993.
[22] D. Robert, Autour de l'approximation semi-classique, Progress in Mathematics, vol. 68, Birkhäuser Boston Inc., Boston, MA, 1987.
Mathematical Reviews (MathSciNet): MR89g:81016
Zentralblatt MATH: 0621.35001
[23] A. Tengstrand, Distributions invariant under an orthogonal group of arbitrary signature, Math. Scand. 8 (1960), 201–218.
Mathematical Reviews (MathSciNet): MR23:A3450
Zentralblatt MATH: 0104.33402
[24] A. Šnirelman, Ergodic properties of eigenfunctions, Uspehi Mat. Nauk 29 (1974), no. 6(180), 181–182.
Mathematical Reviews (MathSciNet): MR53:6648
Zentralblatt MATH: 0324.58020
[25] A. N. Varchenko, Newton polyhedra and estimation of oscillatory integrals, Funct. Anal. Appl. 10 (1976), 175–196.
Zentralblatt MATH: 0351.32011
[26] S. Zelditch, Uniform distribution of eigenfunctions on compact hyperbolic surfaces, Duke Math. J. 55 (1987), no. 4, 919–941.
Mathematical Reviews (MathSciNet): MR89d:58129
Zentralblatt MATH: 0643.58029
Digital Object Identifier: doi:10.1215/S0012-7094-87-05546-3
Project Euclid: euclid.dmj/1077306306
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