Borg-type theorems for matrix-valued Schrödinger operators (Q1585988)

The authors give an extension of Borg's uniqueness theorem [Acta Math. 78, 1-96 (1946; Zbl 0063.00523)] to the one-dimensional Schrödinger equation with a matrix-valued potential that is selfadjoint and locally integrable. By using trace formulas it is shown that, if such potential is reflectionless and the spectrum of the corresponding Hamiltonian is \([0,+\infty),\) then the potential must be trivial.