DIRICHLET PROBLEM FOR DIFFERENTIAL EQUATIONS OF EVEN ORDER OPERATOR COEFFICIENTS THAT CONTAIN AN INVOLUTION
DOI:
https://doi.org/10.31471/2304-7399-2018-2(46)-26-37Keywords:
differential-operator equations, eigenvalue, Riesz base, involution operator, transformation operator.Abstract
We study a problem with Dirichlet conditions for a differential equation of order 2n, whose coefficients are non-self-adjoint operators. It is established that the task operator has two subspaces generated by the involution operator, and two subsystems of the system of eigenfunctions, which are Riesz bases in each of the subspaces. Eigenvalues and eigenfunctions are defined. Sufficient conditions are obtained under which the system of eigenfunctions is the Rees base. The conditions for the existence of unity of the solution of the problem with homogeneous boundary conditions, constructed only as a series on the system of eigenfunctions, are established.
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