On the Non-Self-adjoint Sturm-Liouville Operators in the Space of Vector-Functions

2013/06/06 by Fulya Seref, Seref, Fulya, O. A. Veliev +1
Mathematics · #Algebraic and Geometric Analysis #Differential Equations and Boundary Problems #FOS: Mathematics #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.SP

paper · pdf · doi:10.48550/arxiv.1306.1473

arxiv created 2013/06/06 · openalex publication_date 2013/06/06 · arxiv updated 2013/06/07 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

In this article we obtain asymptotic formulas for the eigenvalues and eigenfunctions of the non-self-adjoint operator generated in space of vector-functions by the Sturm-Liouville equation with m by m matrix potential and the boundary conditions whose scalar case (m=1) are strongly regular. Using these asymptotic formulas, we find a condition on the potential for which the root functions of this operator form a Riesz basis.

Related

• On the Basis Property of the Root Functions of Some Class of Non-self-adjoint Sturm--Liouville Operators
• On the Nonself-adjoint Sturm-Liouville Operator with Matrix Potential
• On the Basis Property of the Root Functions of Sturm-Liouville Operators with General Regular Boundary Conditions
• Asymptotics of the eigenvalues and Abel basis property of the root functions of new type Sturm-Liouville problems
• On the Hill's Operator with Matrix Potential