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

2023/05/29 by Veliev, O. A.
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2305.17986

Abstract

We study the spectrum of the differential operator T generated by the differential expression of order n>2 with the m by m PT-symmetric periodic matrix coefficients. The case when m and n are the odd numbers was investigated in [8]. In this paper, we consider the all remained cases: (a) n is an odd number and m is an even number, (b) n is an even number and m is an arbitrary positive integer. We find conditions on the coefficients under which the spectrum of T in cases (a) and (b) contains respectively large real and positive numbers.

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