Tohoku Mathematical Journal
2025
March
SECOND SERIES VOL. 77, NO. 1

Tohoku Math. J.
77 (2025), 77-91

Title PERTURBATION OF DISCRIMINANT FOR ONE-DIMENSIONAL DISCRETE SCHRÖDINGER OPERATOR WITH COMPLEX-VALUED SPARSE PERIODIC POTENTIAL

Author Masahiro Kaminaga

(Received November 8, 2022, revised March 30, 2023)
Abstract. We consider the one-dimensional discrete Schrödinger operator with complex-valued sparse periodic potential. The spectrum for a complex-valued periodic potential is a complicated compact set in the complex plane represented by real intersections of algebraic curves determined by a discriminant. We represent the discriminant by Chebyshev polynomials and use perturbations of the discriminant to study the spectrum.

Mathematics Subject Classification. Primary 47B28; Secondary 47A55, 47B39.
Key words and phrases. Complex-valued potential, periodic potential.

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