PERTURBATION RESULTS OF SPECTRUM OF STURM-LIOUVILLE DIFFERENTIAL OPERATORS
S. M. Padhye and K. J. Shinde
Department of Mathematics, Shri RLT College of Science, Akola(MS) India.
Department of Mathematics, CAET, Dr. Panjabrao Deshmukh Krishi Vidyapeeth, Akola.
Perturbation results of spectrum of Sturm-Liouville Differential Operators τu(x) = −u′′ (x) + q(x)u(x) defined on (a, b) are obtained. In particular suppose T is a maximal differential operator associated with differential expression τu(x) = −u′′ (x) + q(x)u(x) on L2(a, b) and Tn is a maximal differential operator associated with differential expression τnu = −u′′ (x) + qn(x)u(x) . We determine the sufficient conditions on q and qn to get σ(Tn) → σ(T) and σe (Tn) → σe(T) . Here σ(T) denotes the spectrum of an operator T and σe(T) denotes the essential spectrum of an operator T.
eJournal of Mathematical Sciences, Technology and Humanities
Issue 2, Pages: 973 - 977