Vol. 16, No. 2, 1966

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The deficiency index of ordinary self-adjoint differential operators

Allen Devinatz

Vol. 16 (1966), No. 2, 243–257

This paper is concerned with the computation of the deficiency index of an ordinary self-adjoint differential operator with real coefficients. The operator, L, is supposed defined on [0,) and is regular at the origin. The deficiency index counts the number of L2 solutions to the equation Ly = zy, where z is any nonreal complex number.

The results obtained include as rather special cases almost all of the results known to the author when the order of L is larger than two.

The principal tool used is an asymptotic theorem of N. Levinson.

Mathematical Subject Classification
Primary: 34.20
Received: 24 February 1964
Published: 1 February 1966
Allen Devinatz