On the General Ordinary Quasi-differential Operators with their \(L_{w}^{2}-\) Solutions and their Spectra


In this chapter, we look at the general ordinary quasi-differential expression τ of order n with complex coefficients and its formal adjoint τ_ ^+on the interval [a,b). We will explain in the situation of one unique end-point and under proper conditions that all solutions of a general ordinary quasi-differential equation (τ-λw)u=wf are in the weighted Hilbert space L_w^2 (a,b) provided that all solutions of the equations (τ-λw)u=0 and its adjoint (τ^+-¯λ w)v=0 are in L_w^2 (a,b). It is also possible to derive a variety of results relating to the position of the point spectra and regularity fields of the operators created by such expressions. Some of these findings are expansions or generalizations of those found in the symmetric situation, while others are completely novel.

Author (s) Details:

Sobhy El-Sayed Ibrahim,
Faculty of Basic Education, Department of Mathematics, Public Authority of Applied Education and Training, Kuwait.

Please see the link here: https://stm.bookpi.org/NRAMCS-V5/article/view/7489

Keywords: General ordinary quasi-differential expressions, regular and singular end-points, singular differential operators, essential spectra, point spectra and regularity fields.

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