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- Title
THE NONLOCAL PROBLEM FOR THE DIFFERENTIAL-OPERATOR EQUATION OF THE EVEN ORDER WITH THE INVOLUTION.
- Authors
BARANETSKIJ, YA. O.; KALENYUK, P. I.; KOLYASA, L. I.; KOPACH, M. I.
- Abstract
In this paper, the problem with boundary non-self-adjoint conditions for differential-operator equations of the order 2n with involution is studied. Spectral properties of operator of the problem is investigated. By analogy of separation of variables the nonlocal problemfor the differential-operator equation of the even order is reduced to a sequence {Lk}¥ k=1 of operators of boundary value problems for ordinary differential equations of even order. It is established that each element Lk of this sequence is an isospectral perturbation of the self-adjoint operator L0,k of the boundary value problem for some linear differential equation of order 2n. We construct a commutative group of transformation operators whose elements reflect the system V(L0,k) of the eigenfunctions of the operator L0,k in the system V(Lk) of the eigenfunctions of the operators Lk. The eigenfunctions of the operator L of the boundary value problem for a differential equation with involution are obtained as the result of the action of some specially constructed operator on eigenfunctions of the sequence of operators L0,k. The conditions under which the system of eigenfunctions of the operator L of the studied problem is a Riesz basis is established.
- Subjects
DIFFERENTIAL operators; DIFFERENTIAL equations; BOUNDARY value problems; ABELIAN groups; MATHEMATICAL transformations; ORDINARY differential equations
- Publication
Carpathian Mathematical Publications / Karpats'kì Matematičnì Publìkacìï, 2017, Vol 9, Issue 2, p109
- ISSN
2075-9827
- Publication type
Article
- DOI
10.15330/cmp.9.2.109-119