Generalized eigenvectors of linear operators and biorthogonal systems

Autor:	Ruslan Khats'
Rok vydání:	2022
Předmět:	Mathematics Interdisciplinary Applications Numerical Analysis Applied Mathematics Linear operator generalized eigenvector Bessel function complete system minimal system biorthogonal system Matematik Disiplinler Arası Uygulamalar Analysis
Zdroj:	Volume: 5, Issue: 2 60-71 Constructive Mathematical Analysis
ISSN:	2651-2939
DOI:	10.33205/cma.1077842
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3e1ef75db2374c0e23bb768ce9342e79 https://doi.org/10.33205/cma.1077842 Zobrazit plný text záznamu