2017
Том 69
№ 9

All Issues

Schrödinger Operators with Distributional Matrix Potentials

Molyboga V. M.


Abstract

We study $1D$ Schrödinger operators $L(q)$ with distributional matrix potentials from the negative space $H_{unif}^{− 1} (ℝ, ℂ^{m × m})$. In particular, the class $H_{unif}^{− 1} (ℝ, ℂ^{m × m})$ 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 $q ∈ L_{unif}^{− 1} (ℝ, ℂ^{m × m})$, and also prove that the spectra of operators $L(q)$ belong to the interior of a certain parabola.

English version (Springer): Ukrainian Mathematical Journal 67 (2015), no. 5, pp 748-763.

Citation Example: Molyboga V. M. Schrödinger Operators with Distributional Matrix Potentials // Ukr. Mat. Zh. - 2015. - 67, № 5. - pp. 657–671.