Hostname: page-component-6bf8c574d5-9nwgx Total loading time: 0 Render date: 2025-02-17T18:36:45.087Z Has data issue: false hasContentIssue false
  • English
  • Français

Semibounded Extensions of Singular Ordinary Differential Operators

Published online by Cambridge University Press:  20 November 2018

Allan M. Krall
Allan M. Krall*
Affiliation:
McAllister Building, The Pennsylvania State University university Park, Pennsylvania16802
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The self-adjoint extensions of the singular differential operator Ly = [(py’)’ + qy]/w, where p < 0, w > 0, q ≧ mw, are characterized under limit-circle conditions. It is shown that as long as the coefficients of certain boundary conditions define points which lie between two lines, the extension they help define has the same lower bound.

Keywords

34B2034B25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 31 , Issue 4 , 01 December 1988 , pp. 432 - 438
Copyright
Copyright © Canadian Mathematical Society 1988

References

1. Friedrichs, K. O., Spektral théorie halbbeschrankter operatoren Math. Ann. 109 (1934), pp. 465–487. pp. 685-713.Google Scholar
2. Kaper, H. G. and Kwong, M. K., Regularizing transformations for certain singular Sturm- Liouville boundary value problems SIAM J. Math. Anal. 15 (1984), pp. 957–963.Google Scholar
3. Kaper, H. G., Kwong, M. K. and Zettl, A., Characterizations of the Friedrichs extensions of the singular Sturm-Liouville expressions J. Math. Anal. Appl. 17 (1986), pp. 112–111.Google Scholar
4. Krall, A. M., Shaw, J. K. and Hinton, D. B., Boundary conditions for differential systems in intermediate limit situations Proc. Conf. Diff. Eq., Knowles, I. W. and Lewis, R. T. Eds., Elsevier Science Publ. B.V. (North-Holland) 1984, pp. 301–306.Google Scholar
5. Krall, A. M. and Littlejohn, L. L., Orthogonal polynomials and singular Sturm-Liouville systems, I Rocky Mt. J. Math., to appear.Google Scholar
6. Naimark, M. A., Linear differential operators, part II Frederick Ungar Publ. Co., New York, 1968.Google Scholar
7. Riesz, F. and -Nagy, B. Sz., Functional analysis Frederick Ungar Publ. Co., New York, 1955.Google Scholar
8. Stone, M. H., Linear transformations in Hilbert space Amer. Math. Soc, 1932.Google Scholar