Self-Adjoint Differential-Algebraic Operators With Boundary Terms
Artykbayeva Z. Kanguzhin B.
2026John Wiley and Sons Ltd
Mathematical Methods in the Applied Sciences
2026
In this paper, we introduce a class of self-adjoint differential-algebraic operators with boundary terms. The analytic structure of the resolvent of such an operator is investigated. Explicit representations of the eigenvectors of the initial operator are obtained; these eigenvectors form an orthogonal basis in the space (Formula presented.). The system of eigenvectors is projected onto the subspace (Formula presented.). It is shown that the projected system becomes a Riesz basis in (Formula presented.) only after removing a finite number of functions. A criterion is established that determines which functions should be removed from the projected system to ensure that the remaining functions form a basis.
adjoint operator , boundary value problem , differential-algebraic equation , differential-boundary operator , resolvent
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Al–Farabi Kazakh National University, Almaty, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Al–Farabi Kazakh National University
Institute of Mathematics and Mathematical Modeling
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Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026