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2022•Advanced Studies Euro-Tbilisi Mathematical JournalRequires access

On the spectrum of singular Hahn-Sturm-Liouville operators

Bilender P. Allahverdiev, Hüseyin Tuna

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Abstract

In this paper, we study the spectrum of Hahn-Sturm-Liouville operators. In this context, it is shown that the regular symmetric Hahn-Sturm-Liouville operator is semi-bounded from below. Moreover, we give some conditions for the self-adjoint singular Hahn-Sturm-Liouville operator to have a discrete spectrum. The method of proof is based on the splittings technique. Finally, we investigate the continuous spectrum of this operator.

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What this paper is about

In this paper, we study the spectrum of Hahn-Sturm-Liouville operators. In this context, it is shown that the regular symmetric Hahn-Sturm-Liouville operator is semi-bounded from below. Moreover, we give some conditions for the self-adjoint singular Hahn-Sturm-Liouville operator to have a discrete spectrum. The method of proof is based on the splittings technique. Finally, we investigate the continuous spectrum of this operator.

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Available abstract

In this paper, we study the spectrum of Hahn-Sturm-Liouville operators. In this context, it is shown that the regular symmetric Hahn-Sturm-Liouville operator is semi-bounded from below. Moreover, we give some conditions for the self-adjoint singular Hahn-Sturm-Liouville operator to have a discrete spectrum. The method of proof is based on the splittings technique. Finally, we investigate the continuous spectrum of this operator.

Key concepts: Sturm–Liouville theory, Spectrum (functional analysis), Mathematics, Operator (biology), Bounded function, Context (archaeology), Discrete spectrum, Spectral theory of ordinary differential equations

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