We study 1D Schrödinger operators L(q) with distributional matrix potentials from the negative space H − 1unif (ℝ, ℂ m × m). In particular, the class H − 1unif (ℝ, ℂ m × m) contains periodic and almost periodic generalized functions. We establish the equivalence of different definitions of the operators L(q), investigate their approximation by operators with smooth potentials q ∈ L 1unif (ℝ, ℂ m × m), and also prove that the spectra of operators L(q) belong to the interior of a certain parabola.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 5, pp. 657–671, May, 2015.
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Moliboga, V.N. Schrödinger Operators with Distributional Matrix Potentials. Ukr Math J 67, 748–763 (2015). https://doi.org/10.1007/s11253-015-1112-2
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DOI: https://doi.org/10.1007/s11253-015-1112-2