相关论文: Operator matrices as generators of cosine operator…

Given a bounded linear operator $T$ on separable Hilbert space, we develop an approach allowing one to construct a matrix representation for $T$ having certain specified algebraic or asymptotic structure. We obtain matrix representations…

Some new characterizations of nonnegative Hamiltonian operator matrices are given. Several necessary and sufficient conditions for an unbounded nonnegative Hamiltonian operators to be invertible are obtained; so that the main results in the…

In the present paper, we consider second order strictly hyperbolic linear operators of the form $Lu\,=\,\partial_t^2u\,-\,{\rm div}\big(A(t,x)\nabla u\big)$, for $(t,x)\in[0,T]\times\mathbb{R}^n$. We assume the coefficients of the matrix…

We establish elements of a new approch to ellipticity and parametrices within operator algebras on a manifold with higher singularities, only based on some general axiomatic requirements on parameter-dependent operators in suitable scales…

We give another proof of the $L^p$ boundedness of scattering wave operators, at the low frequency part of the data. The proof also allows the control of the commutator of multiplication by $|x|$ with the wave operator in $L^p$. The method…

We prove that the functions t -> (t^q-1)(t^p-1)^{-1} are operator monotone in the positive half-axis for 0 < p < q < 1, and we calculate the two associated canonical representation formulae. The result is used to find new monotone metrics…

In this paper we consider the wave equations for hypoelliptic homogeneous left-invariant operators on graded Lie groups with time-dependent H\"older propagation speeds. The examples are the time-dependent wave equation for the sub-Laplacian…

The paper develops a theory of spectral boundary value problems from the perspective of general theory of linear operators in Hilbert spaces. An abstract form of spectral boundary value problem with generalized boundary conditions is…

In this work, we study the Hodge wave equation on a compact orientable manifold. We present the necessary differential geometry language to treat Sobolev spaces of differential forms and use these tools to identify a boundary triplet for…

This paper is concerned with robust preconditioning of wave equations constrained linear inverse problems from boundary observation data. The main result of this paper is a concept for regularization parameter robust preconditioning.…

We derive and analyse well-posed boundary conditions for the linear shallow water wave equation. The analysis is based on the energy method and it identifies the number, location and form of the boundary conditions so that the initial…

We investigate the relationship between mapping cones and matrix ordered *-vector spaces (i.e., abstract operator systems). We show that to every mapping cone there is an associated operator system on the space of n-by-n complex matrices,…

We provide a simple sufficient condition in an abstract framework to deduce the existence and completeness of wave operators (resp. modified wave operators) on Sobolev spaces from the existence and completeness of the usual wave operators…

We consider the time-harmonic Maxwell equations at a nonzero wavenumber $k\in\mathbb{C}$ on a bounded and simply connected Lipschitz domain $\Omega$ with an analytic boundary $\Gamma$, on which we impose impedance boundary conditions. We…

We consider the classical Dirac operator on globally hyperbolic manifolds with timelike boundary and show well-posedness of the Cauchy initial-boundary value problem coupled to APS-boundary conditions. This is achieved by deriving suitable…

In this paper we define and construct advanced and retarded Green operators for the wave operator on spacetimes with low regularity. In order to do so we require that the spacetime satisfies the condition of generalised hyperbolicity which…

We study linear damped and viscoelastic wave equations evolving on a bounded domain. For both models, we assume that waves are subject to an inhomogeneous Neumann boundary condition on a portion of the domain's boundary. The analysis of…

We address the problem of integrating operator equations concomitant with the dynamics of non autonomous quantum systems by taking advantage of the use of time-dependent canonical transformations. In particular, we proceed to a discussion…

$L^2$ norm error estimates of semi- and full discretisations, using bulk--surface finite elements and Runge--Kutta methods, of wave equations with dynamic boundary conditions are studied. The analysis resides on an abstract formulation and…

We find simple conditions for a non-negative Hankel quadratic form to be closable. Under some mild a priori assumption on the associated moments these sufficient conditions turn out to be also necessary. We also describe the domain of the…