Discrete spectra criteria for certain classes of singular diffferential and difference operators

• Authors: HILSCHER Roman
• Year of publication: 2001
• Type: Article in Periodical
• Magazine / Source: Computers & mathematics with applications
• MU Faculty or unit: Faculty of Science
• Field: General mathematics
• Keywords: oscillation; property BD; quadratic functional; disconjugacy; Sturm-Liouville equation
• Description: In this paper we consider singular differential and difference operators of the form m(y) = (-1)ⁿ/w(t) (r(t)y⁽ⁿ⁾)⁽ⁿ⁾ and b(y)_k+n = (-1)ⁿ/w_k \Deltaⁿ (r_k \Deltaⁿ y_k) , as well as their full-term analogies. We establish criteria for discreteness and boudnedness bellow of their spectrum -- property BD. Difference operators are studied as the discrete counterparts of the continuous ones.

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