Kyungpook Mathematical Journal 2010; 50(1): 15-35
Published online March 23, 2010
Copyright © Kyungpook Mathematical Journal.
Spectral Analysis of Four Term Differential Operator
Nyamwala Fredrick Oluoch
Fachbereich Mathematik/Informatik, Universität Osnabrück, 49069 Osnabr?uck, Germany
Received: March 23, 2010; Revised: March 23, 2010; Accepted: March 23, 2010
By strengthening dichotomy condition and weakening decay conditions, we show that a four term $2n$-th order differential operator with unbounded coefficients is non-limit-point. Using stringent conditions we show that the deficiency index of this operator is determined by the behaviour of the coefficients themselves. Similarly, we prove the absence of singular continuous spectrum and that the absolutely continuous spectrum has multiplicity two.
Keywords: differential operators, deficiency indices, absolutely continuous spectrum, eigenvalues