Examples of fourth-order scattering-type operators with embedded eigenvalues in their continuous spectra

2021/10/02 by Vassilis G. Papanicolaou, Papanicolaou, Vassilis G.
Mathematics · #47A10 #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2110.00739

openalex publication_date 2021/10/02 · openalex created_date 2021/10/11 · openalex updated_date 2026/07/28

Abstract

We give examples of fourth-order scattering-type operators, acting on L₂(ℝ), which have eigenvalues embedded in their continuous spectra.

Related

• Spectral and scattering theory of fourth order differential operators
• The L^p-boundedness of wave operators for fourth order Schrödinger operators on \mathbb R⁴
• A remark on the absence of eigenvalues in continuous spectra for discrete Schrödinger operators on periodic lattices
• Spectral theory of discontinuous functions of self-adjoint operators and scattering theory
• Spectral and scattering theory of self-adjoint Hankel operators with\n piecewise continuous symbols