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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.

ABSTRACT

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.

 

 

International eJournal of Mathematical Sciences, Technology and Humanities

Volume 3, Issue 2, Pages:  973 - 977