2004/08/04 by Steve Clark, Fritz Gesztesy, Clark, Steve +3
Computer Science · Materials Science · Mathematics · Physics and Astronomy · #34A55 #34B20 #34E05 #34L40 #FOS: Mathematics #FOS: Physical sciences #Lanthanide and Transition Metal Complexes #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math-ph #math.MP #math.SP #msc:34A55 #msc:34B20 #msc:34E05 #msc:34L40
paper · pdf · doi:10.48550/arxiv.math/0408074
27 pages
arxiv created 2004/08/04 · openalex publication_date 2004/08/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Borg-type uniqueness theorems for matrix-valued Jacobi operators H and supersymmetric Dirac difference operators D are proved. More precisely, assuming reflectionless matrix coefficients A, B in the self-adjoint Jacobi operator H=AS+ + A-S- + B (with S^± the right/left shift operators on the lattice Z) and the spectrum of H to be a compact interval [E-,E+], E- < E+, we prove that A and B are certain multiples of the identity matrix. An analogous result which, however, displays a certain novel nonuniqueness feature, is proved for supersymmetric self-adjoint Dirac difference operators D with spectrum given by [-E+1/2,-E-1/2] ∪ [E-1/2,E+1/2], 0 ≤ E- < E+.