Essential Self-Adjointness of Semi-Bounded Schrodinger Operators on Birth-Death Chains

2024/05/24 by Ku, Sean · 1 citation
#05C63 #39A12 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2405.19364

Abstract

We study the essential self-adjointness of semi-bounded Schrödinger operators on birth-death chains. First, we offer a general characterization which originates from studying a second order linear recurrence with variational coefficients which comes from the Schrödinger operator. As this characterization is algebraically complicated, we present an additional theorem discussing the failure of essential self-adjointness. Finally, we study two specific cases of solutions to equations involving the Schrödinger operator over birth-death chains and derive explicit formulas in these cases.

Cited by

• Form uniqueness for graphs with weakly spherically symmetric ends

Related

• Essential self-adjointness of semi-bounded operators
• Essential self-adjointness of the Laplacian on weighted graphs: harmonic functions, stability, characterizations and capacity
• Essential self-adjointness of non-semibounded Schrödinger operators on infinite graphs
• Complete Non-Selfadjointness for Schrödinger Operators on the Semi-Axis
• Spectral Properties of Non-Self-Adjoint Operators in the Semi-classical Regime