The contraction semigroup S (t)= e^ t AS (t)= et A generated by the abstract linear dissipative
evolution equation ̈ u+ A u+ f (A) ̇ u= 0 u¨+ A u+ f (A) u˙= 0 is analyzed, where A is a …

We revisit the damped string equation on a compact interval with a variety of boundary
conditions and derive an infinite sequence of trace formulas associated with it, employing …

We discuss the unitary equivalence of generators GA, R associated with abstract damped
wave equations of the type ̈ u+ R ̇ u+ A^* A u= 0 in some Hilbert space H _1 and certain …

We analyze new phenomena arising in linear damped wave equations on unbounded
domains when the dam** is allowed to become unbounded at infinity. We prove the …

We introduce the new concepts of pseudo numerical range for operator functions and
families of sesquilinear forms as well as the pseudo block numerical range for n× n operator …

We establish a new method for obtaining nonconvex spectral enclosures for operators
associated with second‐order differential equations in a Hilbert space. In particular, we …

The exponential decay rate of the semigroup $ S (t)= e^{t\mathbb {A}} $ generated by the
abstract damped wave equation $$\ddot u+ 2f (A)\dot u+ A u= 0$$ is here addressed, where …

Sign type spectra are an important tool in the investigation of spectral properties of
selfadjoint operators in Krein spaces. It is our aim to show that also sign type spectra for …

The article presents a study regarding the estimation of the decay exponent of an operator
semigroup linked with a second-order linear differential equation. It explores the second …

Variational principles are proved for self-adjoint operator functions arising from variational
evolution equations of the form\[\langle\ddot {z}(t), y\rangle+\mathfrak {d}[\dot {z}(t) …