On a family of differential operators with the coupling parameter in the boundary condition

2005/10/18 by G. Rozenblum, Michael Solomyak, Rozenblum, G. +1
Computer Science · Mathematics · #35P05 (primary) #45B25 #47F05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.math/0510371

openalex publication_date 2005/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a family of differential operators L_α in two variables, depending on the coupling parameter α≥0 that appears only in the boundary conditions. Our main concern is the spectral properties of L_α, which turn out to be quite different for α≤ 1 and for α>1. In particular, L_α has a unique self-adjoint realization for α≤ 1 and many such realizations for α>1. In the more difficult case α>1 an analysis of non-elliptic pseudodifferential operators in dimension one is involved.

Related

• Spectral theory of some non-selfadjoint linear differential operators
• Minimal spectral functions of an ordinary differential operator
• Boundary Data Maps and Krein's Resolvent Formula for Sturm-Liouville Operators on a Finite Interval
• Analysis of Invariants Associated with Spectral Boundary Problems for an Elliptic Operator
• Construction of self-adjoint differential operators with prescribed spectral properties