Related papers: On evolutionary equations related to skew-symmetri…
A simple proof is provided to show that any bounded normal operator on a real Hilbert space is orthogonally equivalent to its transpose(adjoint). A structure theorem for invertible skew-symmetric operators, which is analogous to the finite…
Contraction theory for dynamical systems on Euclidean spaces is well-established. For contractive (resp. semi-contractive) systems, the distance (resp. semi-distance) between any two trajectories decreases exponentially fast. For partially…
The paper extends well-posedness results of a previously explored class of time-shift invariant evolutionary problems to the case of non-autonomous media. The Hilbert space setting developed for the time-shift invariant case can be utilized…
We discuss the spectral properties of collisional semigroups associated to various models from transport theory by exploiting the links between the so-called resolvent approach and the semigroup approach. Precisely, we show that the…
We propose a generalization of the condition for harmonic spatial coordinates analogous to the generalization of the harmonic time slices introduced by Bona et al., and closely related to dynamic shift conditions recently proposed by…
The convergence of various operator splitting procedures, such as the sequential, the Strang and the weighted splitting, is investigated in the presence of a spatial approximation. To this end a variant of Chernoff's product formula is…
We present reduction and reconstruction procedures for the solutions of symmetric stochastic differential equations, similar to those available for ordinary differential equations. Additionally, we use the local tangent-normal…
We consider an abstract class of differential inclusions, which covers differential-algebraic and non-autonomous problems as well as problems with delay. Under weak assumptions on the operators involved, we prove the well-posedness of those…
In this work we begin a theoretical and numerical investigation on the spectra of evolution operators of neutral renewal equations, with the stability of equilibria and periodic orbits in mind. We start from the simplest form of linear…
Despite the strong focus of regularization on ill-posed problems, the general construction of such methods has not been fully explored. Moreover, many previous studies cannot be clearly adapted to handle more complex scenarios, albeit the…
In this paper it is proved that each densely defined $J$-skew-symmetric operator (or each $J$-isometric operator with $\overline{D(A)}=\overline{R(A)}=H$) in a Hilbert space $H$ has a $J$-skew-self-adjoint (respectively $J$-unitary)…
We study evolution equations associated to time-dependent dissipative non-selfadjoint quadratic operators. We prove that the solution operators to these non-autonomous evolution equations are given by Fourier integral operators whose…
We study the problem of convergence to equilibrium for evolution equations associated to general quadratic operators. Quadratic operators are non-selfadjoint differential operators with complex-valued quadratic symbols. Under appropriate…
We consider the initial value Cauchy problem for a class of evolution equations whose Hamiltonian is the Weyl quantization of a homogeneous quadratic form with non-negative definite real part. The solution semigroup is shown to be strongly…
We develop a geometric approach to operator growth and Krylov complexity in many-body quantum systems governed by symmetries. We start by showing a direct link between a unitary evolution with the Liouvillian and the displacement operator…
We study existence, uniqueness, norm estimates and asymptotic time behaviour (in some cases can be claimed to be sharp) for the solution of a general evolutionary integral (differential) equation of scalar type on a locally compact…
It is proved that a general non-differentiable skew convolution semigroup associated with a strongly continuous semigroup of linear operators on a real separable Hilbert space can be extended to a differentiable one on the entrance space of…
We shall deal with the periodic problem for nonlinear perturbations of abstract hyperbolic evolution equations generating an evolution system of contractions. We prove an averaging principle for the translation along trajectories operator…
Evolution algebras are a special class of non-associative algebras exhibiting connections with different fields of Mathematics. Hilbert evolution algebras generalize the concept through a framework of Hilbert spaces. This allows to deal…
Due to the seminal works of Hochbruck and Ostermann exponential splittings are well established numerical methods utilizing operator semigroup theory for the treatment of semilinear evolution equations whose principal linear part involves a…