Schrödinger Operators with Distributional Matrix Potentials

  • V. M. Molyboga

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.
Published
25.05.2015
How to Cite
MolybogaV. M. “Schrödinger Operators With Distributional Matrix Potentials”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, no. 5, May 2015, pp. 657–671, http://umj.imath.kiev.ua/index.php/umj/article/view/2013.
Section
Research articles