Vol. 58, No. 1, 1975

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Second order differential operators with self-adjoint extensions

Arnold Lewis Villone

Vol. 58 (1975), No. 1, 261–266
Abstract

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

      d2-    -d
L = p2dz2 + p1dz + p0

which give rise to symmetric operators in . 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 . 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
Authors
Arnold Lewis Villone