Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-03T08:47:54.615Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonselfadjoint Schrödinger operators with singular first-order coefficients*

Published online by Cambridge University Press:  14 November 2011

Tosio Kato
Tosio Kato
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Synopsis

Schrödinger operators of the form T = (i grad + b(x))2 + a(x) · grad + q(x) in Rm are considered, where a, b ate real vector-valued functions and q is a scalar complex-valued function. It is shown that T is essentially quasi-m-accretive in L2(Rm) if (1 + #x2223;∣)−1a ∈ L4 + L∞, div a ∈ L∞, , and Re q ≧ 0. The proof is elementary.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 96 , Issue 3-4 , 1984 , pp. 323 - 329
Copyright
Copyright © Royal Society of Edinburgh 1984

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.)

References

1Avrin, J.. Thesis, University of California, Berkeley, 1982.Google Scholar
2Wong-Dzung, B.. Lp-theory of degenerate-elliptic and parabolic operators of second order. Proc. Roy. Soc. Edinburgh Sect. A 95 (1983), 95–113.CrossRefGoogle Scholar
3Flanders, H.. Differential Forms (New York: Academic Press, 1963).Google Scholar
4Kato, T., Schrödinger operators with singular potentials. Israel J. Math. 13 (1972), 135–148.Google Scholar
5Leinfelder, H. and Simader, C. G.. Schrödinger operators with singular magnetic vector potentials. Math. Z. 176 (1981), 1–19.Google Scholar
6Simon, B.. Kato's inequality and the comparison of semi-groups. J. Functional Anal. 32 (1979), 97–101.Google Scholar