On the real spectrum of differential operators with PT‐symmetric periodic matrix coefficients

Abstract We study the spectrum of the operator generated by the differential expression of order with the Parity‐Time (PT)‐symmetric periodic matrix coefficients. The case when and are the odd numbers was investigated in [18]. In this paper, we consider the all remained cases: (a) is an odd number and is an even number, (b) is an even number and is an arbitrary positive integer. We find conditions on the coefficients under which in the cases (a) and (b) the spectrum of contains the sets and respectively for some .