Vol. 49, No. 2, 1973

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
Self-adjoint extensions of symmetric differential operators

Arnold Lewis Villone

Vol. 49 (1973), No. 2, 569–577
Abstract

Let denote the Hilbert space of square summable analytic function on the unit disk, and consider those formal differential operators

    ∑n    i
L =    piD
i=0

which give rise to symmetric operators in This paper is devoted to a study of when these operators are actually self-adjoint or admit of self-adjoint extensions in . It is shown that in the first order case the operator is always selfadjoint. For n > 1 sufficient conditions on the pi are obtained for the existence of self-adjoint extensions. In particular a condition on the coefficients is obtained which insures that the operator has defect indices equal to the order of L.

Mathematical Subject Classification 2000
Primary: 47B37
Milestones
Received: 15 September 1972
Revised: 5 January 1973
Published: 1 December 1973
Authors
Arnold Lewis Villone