An analysis of non-selfadjoint first-order differential operators with non-local point interactions

2025/01/20 by Christoph Fischbacher, Danie Paraiso, Fischbacher, Christoph +5 · 1 citation
Computer Science · Mathematics · #34B10 #34L05 #34L10 #47B44 #47E05 #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods for differential equations #Primary: 47B28 #Secondary: 30D99 #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2501.11278

openalex publication_date 2025/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the spectra of non-selfadjoint first-order operators on the interval with non-local point interactions, formally given by i∂_x+V+k⟨ δ,⋅⟩. We give precise estimates on the location of the eigenvalues on the complex plane and prove that the root vectors of these operators form Riesz bases of L²(0,2π). Under the additional assumption that the operator is maximally dissipative, we prove that it can have at most one real eigenvalue, and given any λ∈ℝ, we explicitly construct the unique operator realization such that λ is in its spectrum. We also investigate the time-evolution generated by these maximally dissipative operators.

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• Complete Non-Selfadjointness of Extensions of Symmetric Operators with Bounded Dissipative Perturbations

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