Second order differential operators with self-adjoint extensions

Arnold Lewis Villone

Vol. 58 (1975), No. 1, 261–266

DOI: 10.2140/pjm.1975.58.261

Abstract

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

which give rise to symmetric operators in ℋ. Examples have been given where the symmetric operators associated with these formal operators have defect indices (0,0) and (2, 2) and hence are either self-adjoint or have self-adjoint extensions in ℋ. In this note a class of symmetric operators with defect indices (1, 1) is given.

Mathematical Subject Classification 2000

Primary: 47E05

Secondary: 34B25

Milestones

Received: 27 March 1974

Revised: 24 May 1974

Published: 1 May 1975