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An alternating boundary integral based method for a Cauchy problem for the Laplace equation in semi-infinite regions
Resonances and balls in obstacle scattering with Neumann boundary conditions
1. | Department of Mathematics, University of Missouri, Columbia, Missouri 65211, United States |
References:
[1] |
A. D. Alexandrov, To the theory of mixed volumes of convex bodies part II,, Mat. Sbornik, 2 (1937), 1205. Google Scholar |
[2] |
A. D. Alexandrov, "Selected Works. Part I. Selected Scientific Papers,'', Classics of Soviet Mathematics, (1996).
|
[3] |
C. Bardos, J.-C. Guillot and J. Ralston, La relation de Poisson pour l'équation des ondes dans un ouvert non borné. Application à la théorie de la diffusion,, Comm. Partial Differential Equations, 7 (1982), 905.
doi: 10.1080/03605308208820241. |
[4] |
T. Branson and P. Gilkey, The asymptotics of the Laplacian on a manifold with boundary,, Comm. Partial Differential Equations, 15 (1990), 245.
doi: 10.1080/03605309908820686. |
[5] |
T. Christiansen, Spectral asymptotics for compactly supported perturbations of the Laplacian on Rn,, Comm. Partial Differential Equations, 23 (1998), 933.
doi: 10.1080/03605309808821373. |
[6] |
V. Guillemin and R. B. Melrose, The Poisson summation formula for manifolds with boundary,, Adv. in Math., 32 (1979), 204.
doi: 10.1016/0001-8708(79)90042-2. |
[7] |
A. Hassell and M. Zworski, Resonant rigidity of s2,, J. Funct. Anal., 169 (1999), 604.
doi: 10.1006/jfan.1999.3487. |
[8] |
R. B. Melrose, Scattering theory and the trace of the wave group,, J. Funct. Anal., 45 (1982), 29.
doi: 10.1016/0022-1236(82)90003-9. |
[9] |
R. B. Melrose, Polynomial bound on the number of scattering poles,, J. Funct. Anal., 53 (1983), 287.
doi: 10.1016/0022-1236(83)90036-8. |
[10] |
R. B. Melrose, Polynomial bound on the distribution of poles in scattering by an obstacle,, Journées Équations aux Dérivées partielles (1984), (1984), 1. Google Scholar |
[11] |
R. B. Melrose, "Geometric Scattering Theory,'' Stanford Lectures., Cambridge University Press, (1995).
|
[12] |
V. Petkov and L. Stoyanov, "Geometry of Reflecting Rays and Inverse Spectral Problems,'', Pure and Applied Mathematics (New York). John Wiley & Sons, ().
|
[13] |
V. Petkov and M. Zworski, Semi-classical estimates on the scattering determinant,, Ann. Henri Poincaré, 2 (2001), 675.
doi: 10.1007/PL00001049. |
[14] |
M. Reed and B. Simon, "Methods of Modern Mathematical Physics. IV. Analysis of Operators,'', Academic Press [Harcourt Brace Jovanovich, (1978).
|
[15] |
D. Robert, On the Weyl formula for obstacles,, in, (1995), 264.
|
[16] |
J. Sjöstrand and M. Zworski, Complex scaling and the distribution of scattering poles,, J. Amer. Math. Soc., 4 (1991), 729.
|
[17] |
J. Sjöstrand and M. Zworski, Lower bounds on the number of scattering poles, II,, J. Funct. Anal., 123 (1994), 336.
doi: 10.1006/jfan.1994.1092. |
[18] |
M. E. Taylor, "Partial Differential Equations. II. Qualitative Studies of Linear Equations,'', Applied Mathematical Sciences, (1996).
|
[19] |
M. Zworski, Poisson formulae for resonances,, Séminaire sur les Équations aux Dérivées Partielles, (1997), 1996.
|
[20] |
M. Zworski, Poisson formula for resonances in even dimensions,, Asian J. Math., 2 (1998), 609.
|
show all references
References:
[1] |
A. D. Alexandrov, To the theory of mixed volumes of convex bodies part II,, Mat. Sbornik, 2 (1937), 1205. Google Scholar |
[2] |
A. D. Alexandrov, "Selected Works. Part I. Selected Scientific Papers,'', Classics of Soviet Mathematics, (1996).
|
[3] |
C. Bardos, J.-C. Guillot and J. Ralston, La relation de Poisson pour l'équation des ondes dans un ouvert non borné. Application à la théorie de la diffusion,, Comm. Partial Differential Equations, 7 (1982), 905.
doi: 10.1080/03605308208820241. |
[4] |
T. Branson and P. Gilkey, The asymptotics of the Laplacian on a manifold with boundary,, Comm. Partial Differential Equations, 15 (1990), 245.
doi: 10.1080/03605309908820686. |
[5] |
T. Christiansen, Spectral asymptotics for compactly supported perturbations of the Laplacian on Rn,, Comm. Partial Differential Equations, 23 (1998), 933.
doi: 10.1080/03605309808821373. |
[6] |
V. Guillemin and R. B. Melrose, The Poisson summation formula for manifolds with boundary,, Adv. in Math., 32 (1979), 204.
doi: 10.1016/0001-8708(79)90042-2. |
[7] |
A. Hassell and M. Zworski, Resonant rigidity of s2,, J. Funct. Anal., 169 (1999), 604.
doi: 10.1006/jfan.1999.3487. |
[8] |
R. B. Melrose, Scattering theory and the trace of the wave group,, J. Funct. Anal., 45 (1982), 29.
doi: 10.1016/0022-1236(82)90003-9. |
[9] |
R. B. Melrose, Polynomial bound on the number of scattering poles,, J. Funct. Anal., 53 (1983), 287.
doi: 10.1016/0022-1236(83)90036-8. |
[10] |
R. B. Melrose, Polynomial bound on the distribution of poles in scattering by an obstacle,, Journées Équations aux Dérivées partielles (1984), (1984), 1. Google Scholar |
[11] |
R. B. Melrose, "Geometric Scattering Theory,'' Stanford Lectures., Cambridge University Press, (1995).
|
[12] |
V. Petkov and L. Stoyanov, "Geometry of Reflecting Rays and Inverse Spectral Problems,'', Pure and Applied Mathematics (New York). John Wiley & Sons, ().
|
[13] |
V. Petkov and M. Zworski, Semi-classical estimates on the scattering determinant,, Ann. Henri Poincaré, 2 (2001), 675.
doi: 10.1007/PL00001049. |
[14] |
M. Reed and B. Simon, "Methods of Modern Mathematical Physics. IV. Analysis of Operators,'', Academic Press [Harcourt Brace Jovanovich, (1978).
|
[15] |
D. Robert, On the Weyl formula for obstacles,, in, (1995), 264.
|
[16] |
J. Sjöstrand and M. Zworski, Complex scaling and the distribution of scattering poles,, J. Amer. Math. Soc., 4 (1991), 729.
|
[17] |
J. Sjöstrand and M. Zworski, Lower bounds on the number of scattering poles, II,, J. Funct. Anal., 123 (1994), 336.
doi: 10.1006/jfan.1994.1092. |
[18] |
M. E. Taylor, "Partial Differential Equations. II. Qualitative Studies of Linear Equations,'', Applied Mathematical Sciences, (1996).
|
[19] |
M. Zworski, Poisson formulae for resonances,, Séminaire sur les Équations aux Dérivées Partielles, (1997), 1996.
|
[20] |
M. Zworski, Poisson formula for resonances in even dimensions,, Asian J. Math., 2 (1998), 609.
|
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