Hostname: page-component-7bb8b95d7b-dvmhs Total loading time: 0 Render date: 2024-09-19T19:14:33.395Z Has data issue: false hasContentIssue false
  • English
  • Français

Inequalities and separation for Schrödinger type operators in L2(Rn)*

Published online by Cambridge University Press:  14 November 2011

W. N. Everitt  and
M. Giertz
W. N. Everitt
Affiliation:
Department of Mathematics, University of Dundee
M. Giertz
Affiliation:
Department of Mathematics, The Royal Institute of Technology, Stockholm
Get access Rights & Permissions [Opens in a new window]

Synopsis

The symmetric differential expression M determined by Mf = − Δf;+qf on G, where Δ is the Laplacian operator and G a region of n-dimensional real euclidean space Rn, is said to be separated if qfϵL2(G) for all f ϵ Dt,; here D1 ⊂ L2(G) is the maximal domain of definition of M determined in the sense of generalized derivatives. Conditions are given on the coefficient q to obtain separation and certain associated integral inequalities.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 79 , Issue 3-4 , 1978 , pp. 257 - 265
Copyright
Copyright © Royal Society of Edinburgh 1978

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

1Atkinson, F. V.On some results of Everitt and Giertz. Proc. Roy. Soc. Edinburgh Sect. A. 71 (1972), 151–158.Google Scholar
2Boymatov, K. K.Separation theorems. Dokl. Acad. Nauk SSSR 213 (1973), 1009–1011Google Scholar
3Boymatov, K. K.Separation theorems for the Sturm-Liouville operator. Mat. Zametki 14 (1973), 349–359.Google Scholar
4Everitt, W. N. and Giertz, M.Some properties of the domains of certain differential operators. Proc. London Math. Soc. 23 (1971), 301–324.CrossRefGoogle Scholar
5Everitt, W. N. and Giertz, M.Some inequalities associated with certain ordinary differential operators. Math. Z. 126 (1972), 308–326.CrossRefGoogle Scholar
6Everitt, W. N. and Giertz, M.An example concerning the separation property for differential operators. Proc. Roy. Soc. Edinburgh Sect. A. 71 (1972), 159–165.Google Scholar
7Everitt, W. N. and Giertz, M.Inequalities and separation for certain ordinary differential operators. Proc. London Math. Soc. 28 (1974), 352–372.CrossRefGoogle Scholar
8Everitt, W. N. and Giertz, M.A Dirichlet type result for ordinary differential operators. Math. Ann. 203 (1973), 119–128.CrossRefGoogle Scholar
9Everitt, W. N. and Giertz, M. Inequalities and separation for certain partial differential operators. TRITA-MAT. (Roy. Inst. Tech. Stockholm) 9 (1973), 1–14.Google Scholar
10Everitt, 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.CrossRefGoogle Scholar
11Giertz, M.On the solutions in L 2 (–∞, ∞) of y" + (λ − q)y = 0 when q is rapidly increasing. Proc. London Math. Soc. 14 (1964), 53–73.CrossRefGoogle Scholar
12Jörgens, K.Wesentliche Selbstadjungiertheit singulärer elliptischer Differentialoperatoren zweiter Ordnung in C ∞q(G). Math. Scand. 15 (1964), 5–17.CrossRefGoogle Scholar
13Kato, T.Perturbation theory for linear operators (Berlin: Springer, 1966).Google Scholar
14Yosida, K.Functional analysis (Berlin: Springer, 1966).Google Scholar
15Zettl, A. Separation for differential operators and the L ρ spaces, to appear. (Added 13 July 1977)Google Scholar
16Evans, W. D. and Zettl, A.Dirichlet and separation results for Schrödinger-type operators. Proc. Roy. Soc. Edinburgh Sect. A. 80 (1978), in press.CrossRefGoogle Scholar