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eISSN 0454-8124
pISSN 1225-6951

Original Article

Kyungpook Mathematical Journal 2010; 50(1): 15-35

Published online March 23, 2010

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

Abstract

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