The Schrödinger operator
HTML articles powered by AMS MathViewer
- by Tian Lixin and Liu Zengrong
- Proc. Amer. Math. Soc. 126 (1998), 203-211
- DOI: https://doi.org/10.1090/S0002-9939-98-04014-3
- PDF | Request permission
Abstract:
In this paper we study the maximum dissipative extension of the Schrödinger operator, introduce the generalized indefinite metric space, obtain the representation of the maximum dissipative extension of the Schrödinger operator in the natural boundary space and make preparation for the further study of the longtime chaotic behavior of the infinite-dimensional dynamics system in the Schrödinger equation.References
- Yin Yan, Attractors and dimensions for discretizations of a weakly damped Schrödinger equation and a sine-Gorden [Gordon] equation, Nonlinear Anal. 20 (1993), no. 12, 1417–1452. MR 1225347, DOI 10.1016/0362-546X(93)90168-R
- A. Soffer and M. I. Weinstein, Multichannel nonlinear scattering for nonintegrable equations. II, J. Diff. Eq. 98 (1992), 376–390.
- Nakao Hayashi, The initial value problem for the derivative nonlinear Schrödinger equation in the energy space, Nonlinear Anal. 20 (1993), no. 7, 823–833. MR 1214746, DOI 10.1016/0362-546X(93)90071-Y
- Bernard Helffer, Semi-classical analysis for the Schrödinger operator and applications, Lecture Notes in Mathematics, vol. 1336, Springer-Verlag, Berlin, 1988. MR 960278, DOI 10.1007/BFb0078115
- Guo Qiang Wei and You Qiang Shen, The generalized $p$-normal operators and $p$-hyponormal operators on Banach space, Chinese Ann. Math. Ser. B 8 (1987), no. 1, 70–79. A Chinese summary appears in Chinese Ann. Math. Ser. A 8 (1987), no. 1, 137. MR 886751
- Heinz Langer, Spectral functions of definitizable operators in Kreĭn spaces, Functional analysis (Dubrovnik, 1981) Lecture Notes in Math., vol. 948, Springer, Berlin-New York, 1982, pp. 1–46. MR 672791
- L. Bonger, Indefinite inner product spaces, Springer-Verlag, New York, 1974.
- Peder A. Olsen, Fractional integration, Morrey spaces and a Schrödinger equation, Comm. Partial Differential Equations 20 (1995), no. 11-12, 2005–2055. MR 1361729, DOI 10.1080/03605309508821161
- M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, and N. Nadirashvili, Interior Hölder estimates for solutions of Schrödinger equations and the regularity of nodal sets, Comm. Partial Differential Equations 20 (1995), no. 7-8, 1241–1273. MR 1335750, DOI 10.1080/03605309508821131
- G. Lumer and R. S. Phillips, Dissipative operators in a Banach space, Pacific J. Math. 11 (1961), 679–698. MR 132403, DOI 10.2140/pjm.1961.11.679
- Michael G. Crandall and Ralph S. Phillips, On the extension problem for dissipative operators, J. Functional Analysis 2 (1968), 147–176. MR 0231220, DOI 10.1016/0022-1236(68)90015-3
Bibliographic Information
- Tian Lixin
- Affiliation: Department of Mathematics and Physics, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu, 212013, People’s Republic of China
- Email: lgj@jsust.edu.cn
- Liu Zengrong
- Affiliation: Department of Mathematics, Suzhou University, Suzhou, Jiangsu, 215006, People’s Republic of China
- Received by editor(s): February 28, 1996
- Received by editor(s) in revised form: July 16, 1996
- Additional Notes: Research supported in part by the National Science Foundation of China and Science-technology Foundation of the Ministry of Machine-building Industry of China
- Communicated by: Christopher D. Sogge
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 203-211
- MSC (1991): Primary 46C50, 47A20, 47B39, 47B44, 81Q05
- DOI: https://doi.org/10.1090/S0002-9939-98-04014-3
- MathSciNet review: 1415351