Canonical systems and de Branges spaces [PDF]
arXiv, 2014 This is an exposition of the inverse spectral theory of canonical systems based on de Branges spaces of entire ...
arxiv
Spectral Theory Sum Rules, Meromorphic Herglotz Functions and Large Deviations [PDF]
arXiv, 2016 Short blurb for invited talk at AMS annual meeting in Atlanta; will appear in January AMS ...
arxiv
Landau dispersion relationship in self-consistent field theory [PDF]
arXiv, 2019 The spectral problem is studied associated with Maxwell-Boltzmann equations describing collisionless plasma. Formula for instability index is obtained and effective conditions of two-stream instability are given.
arxiv
The spectral flow, the Fredholm index, and the spectral shift function [PDF]
arXiv, 2007 We discuss the well known ``Fredholm index=spectral flow'' theorem and show that it can be interpreted as a limit case of an identity involving two spectral shift functions.
arxiv
On the spectral estimates for the Schrödinger operator on $\Z^d,\ d\ge3$ [PDF]
arXiv, 2009 For the discrete Schr\"odinger operator we obtain sharp estimates for the number of negative eigenvalues.
arxiv
Stability of Spectral Types for Jacobi Matrices Under Decaying Random Perturbations [PDF]
arXiv, 2007 We study stability of spectral types for semi-infinite self-adjoint tridiagonal matrices under random decaying perturbations. We show that absolutely continuous spectrum associated with bounded eigenfunctions is stable under Hilbert-Schmidt random perturbations. We also obtain some results for singular spectral types.
arxiv
Connectivity and Minimal Distance Spectral Radius of Graphs [PDF]
arXiv, 2010 In this paper, we study how the distance spectral radius behaves when the graph is perturbed by grafting edges. As applications, we also determine the graph with $k$ cut vertices (respectively, $k$ cut edges) with the minimal distance spectral radius.
arxiv
Spectral equality for $C_0$ semigroups [PDF]
arXiv, 2016 In this paper, we give conditions for which the $C_0$ semigroups satisfies spectral equality for semiregular, essentially semiregular and semi-Fredholm spectrum. Also, we establish the spectral inclusion for B-Fredholm spectrum of a $C_0$ semigroups.
arxiv
Transfer functions and local spectral uniqueness for Sturm-Liouville operators, canonical systems and strings [PDF]
arXiv, 2016 It is shown that transfer functions, which play a crucial role in M.G. Krein's study of inverse spectral problems, are a proper tool to formulate local spectral uniqueness conditions.
arxiv
A short nonstandard proof of the Spectral Theorem for unbounded self-adjoint operators [PDF]
arXivBy nonstandard analysis, a very short and elementary proof of the Spectral Theorem for unbounded self-adjoint operators is given.
arxiv