An analysis of non-selfadjoint first-order differential operators with non-local point interactions
Year: 2025
Type: article
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 L 2 ( 0 , 2 π ) . 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.
Institution: Baylor University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4409499519