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

O. A. Veliev

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arXiv · 2305.17986

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

O. A. Veliev

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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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O. A. Veliev. 2023-05-29. On the real spectrum of differential operators with PT-symmetric periodic matrix coefficients. https://arxiv.org/abs/2305.17986

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