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On the Spectra of General Ordinary Quasi-Differential Operators and Their <i>L</i><sup>2</sup><sub><i>w</i></sub>-Solutions
Department of Mathematics, Faculty of Basic Education, Public Authority of Applied Education and Training, Kuwait City, Kuwait
- 1 Department of Mathematics, Faculty of Basic Education, Public Authority of Applied Education and Training, Kuwait City, Kuwait
Advances in Pure Mathematics·Volume 12 (2022)·Pages 186–205·Published 7 March 2022·DOI10.4236/apm.2022.123016
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Abstract
In this paper, we consider the general ordinary quasi-differential expression τ of order n with complex coefficients and its formal adjoint τ + on the interval [ a , b ) . We shall show in the case of one singular end-point and under suitable conditions that all solutions of a general ordinary quasi-differential equation are in the weighted Hilbert space provided that all solutions of the equations and its adjoint are in . Also, a number of results concerning the location of the point spectra and regularity fields of the operators generated by such expressions may be obtained. Some of these results are extensions or generalizations of those in the symmetric case, while the others are new.
KeywordsGeneral Ordinary Quasi-Differential ExpressionsRegular and Singular End-PointsSingular Differential OperatorsEssential SpectraPoint Spectra and Regularity Fields
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