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.
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