Resolvent estimates at low frequencies and limiting amplitude principle for acoustic propagators

Hideo TAMURA

doi:10.2969/jmsj/04140549

Hideo TAMURA

著者情報

ジャーナルフリー

1989 年 41 巻 4 号 p. 549-575

DOI https://doi.org/10.2969/jmsj/04140549

詳細

Published: 1989 Received: 1988/06/22 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) C. O. Bloom, A rate of approach to the steady state of solutions of second-order hyperbolic equations, J. Differential Equations, 19 (1975), 296-329.
2) M. S. P. Eastham and H. Kalf, Schrödinger-type operators with continuous spectra, Reseach note in Math., 65, Pitman, Boston•London•Melbourne, 1982.
3) D. M. Eidus, The principle of limiting amplitude, Russian Math. Surveys, 24 (1969), 97-167.
4) R. Froese and I. Herbst, Exponential bounds and absence of positive eigenvalues for N-body Schrödinger operators, Comm. Math. Phys., 87 (1982), 429-447.
5) L. Hörmander, The analysis of linear partial differential operators IV, Springer, 1984.
6) A. Jensen and T. Kato, Spectral properties of Schrödinger operators and time-decay of the wave functions, Duke Math. J., 46 (1979), 583-611.
7) A. Jensen, E. Mourre and P. Perry, Multiple commutator estimates and resolvent smoothness in quantum scattering theory, Ann. Inst. H. Poincaré Phys. Théor., 41 (1984), 207-225.
8) K. Mochizuki, Growth properties of solutions of second order elliptic differential equations, J. Math. Kyoto Univ., 16 (1976), 351-373.
9) E. Mourre, Absence of singular continuous spectrum for certain selfadjoint operators, Comm. Math. Phys., 76 (1981), 391-408.
10) M. Murata, Asymptotic expansions in time for solutions of Schrödinger-type equations, J. Func. Anal. Appl., 49 (1982), 10-56.
11) P. Perry, I. M. Sigal and B. Simon, Spectral analysis of N-body Schrödinger operators, Ann. of Math., 114 (1981), 519-567.
12) H. Tamura, Principle of limiting absorption for N-body Schrödinger operators, -a remark on the commutator method-, Lett. Math. Phys., 17 (1989), 31-36.
13) J. Uchiyama, Polynomial growth or decay of eigenfunctions of second-order elliptic operators, Publ. RIMS. Kyoto Univ., 23 (1987), 975-1006.

Right : [1] C. O. Bloom, A rate of approach to the steady state of solutions of second-order hyperbolic equations, J. Differential Equations, 19 (1975), 296-329.
[2] M. S. P. Eastham and H. Kalf, Schrödinger-type operators with continuous spectra, Reseach note in Math., 65, Pitman, Boston·London·Melbourne, 1982.
[3] D. M. Eidus, The principle of limiting amplitude, Russian Math. Surveys, 24 (1969), 97-167.
[4] R. Froese and I. Herbst, Exponential bounds and absence of positive eigenvalues for N-body Schrödinger operators, Comm. Math. Phys., 87 (1982), 429-447.
[5] L. Hörmander, The analysis of linear partial differential operators IV, Springer, 1984.
[6] A. Jensen and T. Kato, Spectral properties of Schrödinger operators and time-decay of the wave functions, Duke Math. J., 46 (1979), 583-611.
[7] A. Jensen, E. Mourre and P. Perry, Multiple commutator estimates and resolvent smoothness in quantum scattering theory, Ann. Inst. H. Poincaré Phys. Théor., 41 (1984), 207-225.
[8] K. Mochizuki, Growth properties of solutions of second order elliptic differential equations, J. Math. Kyoto Univ., 16 (1976), 351-373.
[9] E. Mourre, Absence of singular continuous spectrum for certain selfadjoint operators, Comm. Math. Phys., 76 (1981), 391-408.
[10] M. Murata, Asymptotic expansions in time for solutions of Schrödinger-type equations, J. Func. Anal. Appl., 49 (1982), 10-56.
[11] P. Perry, I. M. Sigal and B. Simon, Spectral analysis of N-body Schrödinger operators, Ann. of Math., 114 (1981), 519-567.
[12] H. Tamura, Principle of limiting absorption for N-body Schrödinger operators, -a remark on the commutator method-, Lett. Math. Phys., 17 (1989), 31-36.
[13] J. Uchiyama, Polynomial growth or decay of eigenfunctions of second-order elliptic operators, Publ. RIMS. Kyoto Univ., 23 (1987), 975-1006.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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