We prove new enclosures for the spectrum of non-selfadjoint operator matrices associated with second order linear differential equations z̈(t) +Dż(t) +A0z(t) = 0 in a Hilbert space. Our main tool is the quadratic numerical range for which we establish the spectral inclusion property under weak assumptions on the operators involved; in particular, the damping operator only needs to be accretive a...

We extend to infinite dimensional separable Hilbert spaces the Schur convexity property 13 of eigenvalues of a symmetric matrix with real entries. Our framework includes both the case of linear, selfadjoint, compact operators, and that of linear selfadjoint operators 15 that can be approximated by operators of finite rank and having a countable family of eigenvalues. The abstract results of the...

We study the essential self-adjointness for real principal type differential operators. Unlike elliptic case, we need geometric conditions even operators on Euclidean space with asymptotically constant coefficients, and prove under null non-trapping condition.

For a class of bounded random selfadjoint operators (Lu)(n) =

The classical theory of reduction, initiated by Weierstrass, has found modern applications to the fields of Integrable Systems and Number Theory, to name but two. In this short note we only address specific cases, providing minimal historical references, listing the steps that we devised, and exhibiting some new explicit formulas. A full-length discussion of original motivation, theoretical adv...