Article contents
Dirichlet and separation results for Schrödinger-type operators
Published online by Cambridge University Press: 14 November 2011
Synopsis
Conditions are obtained which ensure that the maximal operator generated by the formally self-adjoint second-order differential expression
in L2(Rn), n ≥ 1 has the Dirichlet and separation properties.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 80 , Issue 1-2 , 1978 , pp. 151 - 162
- Copyright
- Copyright © Royal Society of Edinburgh 1978
References
1Atkinson, F. V.On some results of Everitt and Giertz. Proc. Roy. Soc. Edinburgh Sect. A. 71 (1973), 151–158.Google Scholar
2Atkinson, F. V.Limit-n criteria of integral type. Proc. Roy. Soc. Edinburgh Sect. A 73 (1975), 167–198.Google Scholar
3Eastham, M. S. P., Evans, W. D. and McLeod, J. B.The essential self-adjointness of Schrödinger-type operators. Arch. Rational Mech. Anal. 60 (1976), 185–204.Google Scholar
4Evans, W. D. On limit-point and Dirichlet-type results for second-order differential expressions. Lecture Notes in Mathematics 564 (Berlin: Springer, 1976).Google Scholar
5Evans, W. D.On the essential self-adjointness of powers of Schrödinger-type operators, Proc. Roy. Soc. Edinburgh Sect. A 79 (1977), 61–77.Google Scholar
6Everitt, W. N., Giertz, M. and Weidmann, J.Some remarks on a separation and limit-point criterion of second-order ordinary differential expressions. Math. Ann. 200 (1973), 335–346.Google Scholar
7Everitt, W. N. and Giertz, M.An example concerning the separation property of differential operators. Proc. Roy. Soc. Edinburgh Sect. A 71 (1973), 159–165.Google Scholar
8Everitt, W. N. and Giertz, M.Inequalities and separation for certain ordinary differential operators. Proc. London Math. Soc. 28 (1974), 352–372.Google Scholar
9Everitt, W. N. and Giertz, M. Inequalities and separation for certain partial differential expressions, preprint.Google Scholar
10Kato, T.Schrödinger operators with singular potentials. Israel J. Math. 13 (1972), 135–148.Google Scholar
11Knowles, I. On essential self-adjointness of singular elliptic differential operators, preprint.Google Scholar
12Read, T. T.A limit-point criterion for expressions with intermittently positive co-efficients. /. London Math. Soc., 15 (1977), 271–276.Google Scholar
13Kalf, H.Self-adjointness for strongly singular potentials with a −|x|2 fall-off at infinity. Math. Z. 133 (1973), 249–255.Google Scholar
14Kato, T.A second look at the essential self-adjointness of the Schrödinger operator. Physical Reality and Mathematical Description. (Dordrecht: Reidel, 1974).Google Scholar
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