Vol. 59, No. 1, 1975

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ISSN: 0030-8730
A class of symmetric differential operators with deficiency indices (1, 1)

Arnold Lewis Villone

Vol. 59 (1975), No. 1, 295–301
Abstract

Let denote the Hilbert space of analytic functions on the unit disk which are square summable with respect to the usual area measure. In this paper we show that every symmetric differential operator of order two or more having the form L = t=0n(ai+1(i)zi+1 + ai1(i)zi1)Dt,a1(0) = 0, has defect indices (1, 1) and hence has self-adjont extensions in . We are also able to show that L + M has defect indices (1,1) where M is a symmetric Euler operator of order n1,M = sumi=0n1biziDi, provided that |bn1| < (n 1)|an+1(n)|.

Mathematical Subject Classification 2000
Primary: 47E05
Secondary: 34B25
Milestones
Received: 1 April 1975
Published: 1 July 1975
Authors
Arnold Lewis Villone