@article{article_1077842, title={Generalized eigenvectors of linear operators and biorthogonal systems}, journal={Constructive Mathematical Analysis}, volume={5}, pages={60–71}, year={2022}, DOI={10.33205/cma.1077842}, author={Khats’, Ruslan}, keywords={Linear operator, generalized eigenvector, Bessel function, complete system, minimal system, biorthogonal system}, abstract={The notions of a set of generalized eigenvalues and a set of generalized eigenvectors of a linear operator in Euclidean space are introduced. In addition, we provide a method to find a biorthogonal system of a subsystem of eigenvectors of some linear operators in a Hilbert space whose systems of canonical eigenvectors are over-complete. Related to our problem, we will show an example of a linear differential operator that is formally adjoint to Bessel-type differential operators. We also investigate basis properties (completeness, minimality, basicity) of the systems of generalized eigenvectors of this differential operator.}, number={2}, publisher={Tuncer ACAR}