Vol. 68, No. 2, 1977

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The deficiency index of a third order operator

Richard Carl Gilbert

Vol. 68 (1977), No. 2, 369–392
Abstract

Let L be a formally selfadjoint third order linear ordinary differential operator defined on [r,). Using a method of Fedorjuk, asymptotic formulas are found for the solutions of Ly = iσy, σ0. These formulas are used to determine the deficiency index of L when L has polynomial coefficients. As a consequence, the deficiency index is determined for values of the parameters involved for which it has not previously been determined.

Mathematical Subject Classification 2000
Primary: 34C99
Secondary: 34E05
Milestones
Received: 4 September 1974
Revised: 1 March 1976
Published: 1 February 1977
Authors
Richard Carl Gilbert