High energy resolvent estimates, I, first order operators

Minoru MURATA

doi:10.2969/jmsj/03540711

Minoru MURATA

著者情報

ジャーナルフリー

1983 年 35 巻 4 号 p. 711-733

DOI https://doi.org/10.2969/jmsj/03540711

詳細

Published: 1983 Received: 1982/04/09 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) L. Hörmander, The existence of wave operators in scattering theory, Math. Z., 146 (1976), 69-91.
2) H. Kumano-go, A calculus of Fourier integral operators on Rⁿ and the fundamental solution for an operator of hyperbolic type, Comm. Partial Differential Equations, 1 (1976), 1-44.
3) H. Kumano-go and M. Nagase, Pseudo-differential operators with non-regular symbols and applications, Funkcialaj Ekvacioj, 21(1978), 151-192.
4) P. D. Lax and R. S. Phillips, Scattering Theory, Academic Press, New York, 1967.
5) R. B. Melrose, Singularities and energy decay in acoustic scattering, Duke Math. J., 46(1979), 43-59.
6) C. H. Morawetz, J. V. Ralston, and W. A. Strauss, Decay of solutions of the wave equation outside nontrapping obstacles, Comm. Pure Appl. Math., 30 (1977), 447-508.
7) M. Murata, Rate of decay of local energy and spectral properties of elliptic operators, Japan. J. Math., 6(1980), 77-127.
8) J. V. Ralston, Local decay of solutions of conservative first order hyperbolic systems in odd dimensional space, Trans. Amer. Math. Soc., 194(1974), 27-51.
9) J. Rauch, Asymptotic behavior of solutions to hyperbolic partial differential equations with zero speeds, Comm. Pure Appl. Math., 31(1978), 431-480.
10) B. Vainberg, On the short wave asymptotic behavior of solutions of stationary problems and the asymptotic behavior as t→∞ of solutions of non-stationary problems, Russian Math. Surveys, 30; 2 (1975), 1-58.

Right : [1] L. Hörmander, The existence of wave operators in scattering theory, Math. Z., 146 (1976), 69-91.
[2] H. Kumano-go, A calculus of Fourier integral operators on Rⁿ and the fundamental solution for an operator of hyperbolic type, Comm. Partial Differential Equations, 1 (1976), 1-44.
[3] H. Kumano-go and M. Nagase, Pseudo-differential operators with non-regular symbols and applications, Funkcialaj Ekvacioj, 21 (1978), 151-192.
[4] P. D. Lax and R. S. Phillips, Scattering Theory, Academic Press, New York, 1967.
[5] R. B. Melrose, Singularities and energy decay in acoustic scattering, Duke Math. J., 46 (1979), 43-59.
[6] C. H. Morawetz, J. V. Ralston, and W. A. Strauss, Decay of solutions of the wave equation outside nontrapping obstacles, Comm. Pure Appl. Math., 30 (1977), 447-508.
[7] M. Murata, Rate of decay of local energy and spectral properties of elliptic operators, Japan. J. Math., 6 (1980), 77-127.
[8] J. V. Ralston, Local decay of solutions of conservative first order hyperbolic systems in odd dimensional space, Trans. Amer. Math. Soc., 194 (1974), 27-51.
[9] J. Rauch, Asymptotic behavior of solutions to hyperbolic partial differential equations with zero speeds, Comm. Pure Appl. Math., 31 (1978), 431-480.
[10] B. Vainberg, On the short wave asymptotic behavior of solutions of stationary problems and the asymptotic behavior as t→∞ of solutions of non-stationary problems, Russian Math. Surveys, 30; 2 (1975), 1-58.

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

責任著者(Corresponding author)

訂正情報

J-STAGEへの登録はこちら（無料）