Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-26T20:16:28.426Z Has data issue: false hasContentIssue false
  • English
  • Français

12.—Sequences of Deficiency Indices*

Published online by Cambridge University Press:  14 February 2012

T. T. Read
T. T. Read
Affiliation:
Department of Mathematics, University of Dundee.
Get access Rights & Permissions [Opens in a new window]

Synopsis

An explicit characterisation is given of those sequences of positive integers which occur as the deficiency indices associated with the sequence of powers of some formally symmetric 2nth order real differential expression on [0, ∞) which is regular at 0.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 74 , 1976 , pp. 157 - 164
Copyright
Copyright © Royal Society of Edinburgh 1976

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

1Chaudhuri, J. and Everitt, W. N.. On the square of a formally self-adjoint differential expression. J. London Math. Soc. 1 (1969), 661–673.Google Scholar
2Everitt, W. N. and Giertz, M.. On some properties of the powers of a formally self-adjoint differential expression. Proc. London Math. Soc. 24 (1972), 149–170.Google Scholar
3Everitt, W. N. and Giertz, M.. On the integrable-square classification of ordinary symmetric differential expressions. J.London Math. Soc. 10 (1975), 417–426.Google Scholar
4Glazman, I. M.. On the theory of singular differential operators. Amer. Math. Soc. Transl. 4 (1962), 331–372.Google Scholar
5Kauffman, R. M.. A rule relating the deficiency index of Lj to that of Lk. Proc. Roy. Soc. Edinburgh Sect. A 74 (1976), 115–118.Google Scholar
6Kauffman, R. M.. Polynomials and the limit point condition. Trans. Amer. Math. Soc. 201 (1975), 347–366.Google Scholar
7Kumar, V. K.. A criterion for a formally symmetric fourth order differential expression to be in the limit-2 case at ∞. J. London Math. Soc. 8 (1974), 134–138.Google Scholar
8Naimark, M. A.. Linear differential operators, II (New York: Ungar,1968).Google Scholar
9Read, T. T.. On the limit point condition for polynomials in a second order differential expression. J. London Math. Soc. 10 (1975), 357–366.Google Scholar
10Zettl, A.. The limit point and limit circle cases for polynomials in a differential operator. Proc. Roy. Soc. Edinburgh Sect. A 72 (1975), 219–224.Google Scholar