Lieb–Thirring inequalities for generalized magnetic fields

• DOI: 10.1007/s13373-015-0067-9
• Publication Date: 2015-03-13T12:25:17Z
• Authors: Oscar Mickelin
• Keywords: Operator (biology); Matrix (chemical analysis)

Following an approach by Exner et al. (Commun Math Phys 26:531–541, 2014), we establish Lieb–Thirring inequalities for general self-adjoint and second-degree differential operators with matrix valued potentials acting in one space-dimension. These include generalize the magnetic Schrödinger operator. Three different settings are considered, functions defined on whole real line, a semi-axis interval, respectively, leading to types of bounds. An interpretation result terms star graphs two vertices is also given.