Kato – Kuroda Theorems for a Large Class of Perturbations

@inproceedings{Ionescu2009KatoK,
  title={Kato – Kuroda Theorems for a Large Class of Perturbations},
  author={A D Ionescu and W. Schlag},
  year={2009}
}
We prove asymptotic completeness for operators of the form H = −∆+L on L(R), d ≥ 2, where L is an admissible perturbation. Our class of admissible perturbations contains multiplication operators defined by real-valued potentials V ∈ L(R), q ∈ [d/2, (d + 1)/2] (if d = 2 then we require q ∈ (1, 3/2]), as well as real-valued potentials V satisfying a global Kato condition. The class of admissible perturbations also contains first order differential operators of the form ~a · ∇−∇ ·~a for suitable… CONTINUE READING

From This Paper

Topics from this paper.
7 Citations
15 References
Similar Papers

References

Publications referenced by this paper.
Showing 1-10 of 15 references

Spectral properties of Schrödinger operators and scattering theory

  • S. Agmon
  • Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 2
  • 1975
Highly Influential
16 Excerpts

B

  • M. Reed
  • Simon Methods of modern mathematical physics. IV…
  • 1978
Highly Influential
5 Excerpts

Wave operators and similarity for some non-selfadjoint operators

  • T. Kato
  • Math. Ann. 162
  • 1966
Highly Influential
6 Excerpts

On the absence of positive eigenvalues of Schrödinger operators with rough potentials

  • A. D. Ionescu, D. Jerison
  • Geom. Funct. Anal. 13
  • 2003
2 Excerpts

Harmonic Analysis: Real-Variable Methods

  • E. M. Stein
  • Orthogonality, and Oscillatory Integrals…
  • 1993

Schrödinger operators with application to quantum mechanics and global geometry

  • H. Cycon, R. Froese, W. Kirsch, B. Simon
  • Texts and Monographs in Physics. Springer Study…
  • 1987
1 Excerpt

Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators

  • C. E. Kenig, A. Ruiz, C. D. Sogge
  • Duke Math. J. 55
  • 1987

Oscillatory integrals in Fourier analysis

  • E. M. Stein
  • Beijing Lectures in Harmonic Analysis, Annals of…
  • 1986

Similar Papers

Loading similar papers…