2011/12/13 by Alexander V. Kiselev, Serguei Naboko, Kiselev, Alexander V. +1
Computer Science · Mathematics · #FOS: Mathematics #Matrix Theory and Algorithms #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.SP
paper · pdf · doi:10.48550/arxiv.1112.3001
arxiv created 2011/12/13 · openalex publication_date 2011/12/13 · arxiv updated 2011/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove an analogue to the Cayley identity for an arbitrary self-adjoint operator in a Hilbert space. We also provide two new ways to characterize vectors belonging to the singular spectral subspace in terms of the analytic properties of the resolvent of the operator, computed on these vectors. The latter are analogous to those used routinely in the scattering theory for the absolutely continuous subspace.