Generalized eigenvectors of linear operators and biorthogonal systems

Year 2022, Volume: 5 Issue: 2, 60 - 71, 15.06.2022

Ruslan Khats'

https://doi.org/10.33205/cma.1077842

Cited By: 2

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.

Keywords

Linear operator, generalized eigenvector, Bessel function, complete system, minimal system, biorthogonal system

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