Generalized eigenvectors of linear operators and biorthogonal systems

Authors : Ruslan KHATS`

Pages : 60-71

Doi:10.33205/cma.1077842

View : 14 | Download : 4

Publication Date : 2022-06-15

Article Type : Research Paper

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 insert ignore into journalissuearticles values(completeness, minimality, basicity); of the systems of generalized eigenvectors of this differential operator.
Keywords : Linear operator, generalized eigenvector, Bessel function, complete system, minimal system, biorthogonal system