References
- Melrose, R. B. (1995). Geometric Scattering Theory. Cambridge: Cambridge University Press.
- Dyatlov, D., Zworski, N. Mathematical theory of scattering resonances. (in press)
- Reed, M., Simon, B. (1979). Methods of Modern Mathematical Physics. III. New York: Academic Press [Harcourt Brace Jovanovich Publishers].
- Taylor, M. E. (2011). Partial Differential Equations II. Qualitative Studies of Linear Equations. Applied Mathematical Sciences, Vol. 116, 2nd ed. New York: Springer.
- Gell-Redman, J., Hassell, A., Zelditch, S. (2015). Equidistribution of phase shifts in semiclassical potential scattering. J. Lond. Math. Soc. 91(1):159–179.
- Melrose, R. B. (1988). Weyl asymptotics for the phase in obstacle scattering. Commun. Partial Diff. Equat. 13(11):1431–1439.
- Majda, A., Ralston, J. (1978). An analogue of Weyl’s theorem for unbounded domains. I. Duke Math. J. 45(1):183–196.
- Robert, D. (1996). On the Weyl formula for obstacles. In Partial Differential Equations and Mathematical Physics (Copenhagen, 1995; Lund, 1995). Progr. Nonlinear Differential Equations Appl., Vol. 21. Boston, MA: Birkhäuser Boston, pp. 264–285.
- Eckmann, J.-P., Pillet, C.-A. (1995). Spectral duality for planar billiards. Commun Math. Phys. 170(2):283–313.
- Ivrii, V. (1980). Second term of the spectral asymptotic expansion of the Laplace-Beltrami operator on manifolds with boundary. Funct. Anal. Appl. 14(2):98–106.
- Birman, M. S., Yafaev, D. R. (1984). Asymptotic behaviour of the spectrum of the scattering matrix. J. Math. Sci. 25(1):793–814.
- Sobolev, A. V., Yafaev, D. R. (1985). Phase analysis in the problem of scattering by a radial potential. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 147:155–178, 206. Boundary value problems of mathematical physics and related problems in the theory of functions, No. 17.
- Ingremeau, M. (2016). Equidistribution of phase shifts in trapped scattering. J Spectral Theory. arXiv:1602.00141.
- Bulger, D., Pushnitski, A. (2012). The spectral density of the scattering matrix for high energies. Commun. Math. Phys. Phys. 316(3):693–704.
- Datchev, K., Gell-Redman, J., Hassell, A., Humphries, P. (2013). Approximation and equidistribution of phase shifts: spherical symmetry. Commun. Math. Phys. 326(1):209–236.
- Nakamura, S., Pushnitski, A. (2013). The spectrum of the scattering matrix near resonant energies in the semiclassical limit. Trans. Am. Math. Soc. 366(4):1725–1747.
- Zelditch, S. (1992). Kuznecov sum formulae and Szegő limit formulae on manifolds. Commun. Partial Diff. Equat. 17(1–2):221–260.
- Zelditch, S. (1997). Index and dynamics of quantized contact transformations. Ann. Inst. Fourier (Grenoble) 47(1):305–363.
- Melrose, R. B., Taylor, M. E. (1985). Near peak scattering and the corrected Kirchhoff approximation for a convex obstacle. Adv. Math. 55(3):242–315.
- Gell-Redman, J., Hassell, A. (2015). The distribution of phase shifts for semiclassical potentials with polynomial decay. arXiv:1509:03468.
- Petkov, V., Stojanov, L. (1988). On the number of periodic reflecting rays in generic domains. Ergod. Theory Dynam. Syst. 8(1):81–91.
- Safarov, Y., Vassilev, D. (1997). The Asymptotic Distribution of Eigenvalues of Partial Differential Operators, Vol. 155. Providence, RI: American Mathematical Society.
- Helton, J. W., Ralston, J. V. (1976). The first variation of the scattering matrix. J. Diff. Equat. 21(2):378–394.
- Ingremeau, M. (2016). The semi-classical scattering matrix from the point of view of Gaussian states. arXiv:1612.06783.
- Christiansen, T. J. (2015). A sharp lower bound for a resonance-counting function in even dimensions. J. Spectr. Theory Theory 5(3):571.
- Zworski, M. (1989). Sharp polynomial bounds on the number of scattering poles. Duke Math. J. 59(2):311–323.
- Höormander, L. (1983). The Analysis of Linear Partial Differential Operators. I. Classics in Mathematics. Berlin: Springer-Verlag.