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

2025/09/24 by Fischbacher, Christoph, López, Andrés Felipe Patiño, Winklmeier, Monika
#47A20 #47B28 (Secondary) #47B44 (Primary) 47E05 #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2509.19806

Abstract

Using boundary triples, we develop an abstract framework to investigate the complete non-selfadjointness of the maximally dissipative extensions of dissipative operators of the form S+iV, where S is symmetric with equal finite defect indices and V is a bounded non-negative operator. Our key example is the dissipative Schrödinger operator -\tfracd²dx²+i V on the interval.

Citations

• An analysis of non-selfadjoint first-order differential operators with non-local point interactions
• The spectral form of the functional model for maximally dissipative operators: A Lagrange identity approach
• Complete Non-Selfadjointness for Schrödinger Operators on the Semi-Axis
• The Non-Proper Dissipative Extensions of a Dual Pair
• The Proper Dissipative Extensions of a Dual Pair

Related

• Complete Non-Selfadjointness for Schrödinger Operators on the Semi-Axis
• Maximally dissipative and self-adjoint extensions of K-invariant operators
• The Non-Proper Dissipative Extensions of a Dual Pair
• Non-symmetric perturbations of self-adjoint operators
• On the Weyl-Titchmarsh and Livšic functions