Hostname: page-component-7dd5485656-s6l46 Total loading time: 0 Render date: 2025-10-31T13:20:35.639Z Has data issue: false hasContentIssue false
  • English
  • Français

On the absolutely continuous subspaces of Floquet operators

Published online by Cambridge University Press:  14 November 2011

Min-Jei Huang
Min-Jei Huang
Affiliation:
Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 30043
Get access Rights & Permissions [Opens in a new window]

Abstract

The purpose of this paper is to describe various subspaces that are closely related to the absolutely continuous subspace of a Floquet operator. This paper generalises and extends several known results.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 4 , 1994 , pp. 703 - 712
Copyright
Copyright © Royal Society of Edinburgh 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1Enss, V. and Veselić, K.. Bound states and propagating states for time-dependent Hamiltonians. Ann. Inst. H. Poincaré, Physique Théorique 39 (1983), 159–191.Google Scholar
2Howland, J. S.. Stationary scattering theory for time-dependent Hamiltonians. Math. Ann. 207 (1974), 315–335.CrossRefGoogle Scholar
3Howland, J. S.. Scattering theory for Hamiltonians periodic in time. Indiana Univ. Math. J. 28 (1979), 471–494.CrossRefGoogle Scholar
4Huang, M.-J.. A trace theorem for time-periodic Hamiltonian operators. J. Math. Anal. Appl. 143 (1989), 224–234.CrossRefGoogle Scholar
5Huang, M.-J.. Absence of bound states in a class of time-dependent Hamiltonians J. Math. Anal. Appl. 182 (1994), to appear.Google Scholar
6Huang, M.-J. and Lavine, R. B.. Boundedness of kinetic energy for time-dependent Hamiltonians. Indiana Univ. Math. J. 38 (1989), 189–210.CrossRefGoogle Scholar
7Kato, T.. Perturbations of continuous spectra by trace-class operators. Proc. Japan Acad. 33 (1957), 260–264.Google Scholar
8Kato, T.. Wave operators and similarity for some non-selfadjoint operators. Math. Ann. 162 (1966), 258–279.CrossRefGoogle Scholar
9Kato, T.. Linear evolution equations of hyperbolic type, I, II. J. Fac. Sci. Univ. Tokyo, Sec. IA Math. 17 (1970), 241–258; J. Math. Soc. Japan 25 (1973), 648–666.Google Scholar
10Kato, T.. Perturbation Theory for Linear Operators (Berlin: Springer, 1980).Google Scholar
11Reed, M. and Simon, B.. Methods of Modern Mathematical Physics II, Fourier Analysis, Self-Adjointness (New York: Academic Press, 1975).Google Scholar
12Reed, M. and Simon, B.. Methods of Modern Mathematical Physics III, Scattering Theory (New York: Academic Press, 1979).Google Scholar
13Rosenblum, M.. Perturbation of the continuous spectrum and unitary equivalence. Pacific J. Math. 7 (1957), 997–1010.CrossRefGoogle Scholar
14Yajima, K.. Scattering theory for Schrödinger equations with potentials periodic in time. J. Math. Soc. Japan 29 (1977), 729–743.CrossRefGoogle Scholar
15Yajima, K. and Kitada, H.. Bound states and scattering states for time-periodic Hamiltonians. Ann. Inst. H. Poincaré, Physique Théorique 39 (1983), 145–157.Google Scholar