相关论文: m-Accretive Extensions of Friedrichs Operators

The theory of abstract Friedrichs operators was introduced some fifteen years ago with the aim of providing a more comprehensive framework for the study of positive symmetric systems of first-order partial differential equations, nowadays…

In our article [15] description in terms of abstract boundary conditions of all $m$-accretive extensions and their resolvents of a closed densely defined sectorial operator $S$ have been obtained. In particular, if $\{\mathcal{H},\Gamma\}$…

We discuss the detectable subspaces of an operator. We analyse the relation between the M-function (the abstract Dirichlet to Neumann map) and the resolvent bordered by projections onto the detectable subspaces. The abstract results are…

There has been significant developments in the classification of boundary conditions of positive symmetric systems, also known as Friedrichs systems, after the introduction of operator theoretic framework. We take a step forward towards…

The theory of abstract Friedrichs operators, introduced by Ern, Guermond and Caplain (2007), proved to be a successful setting for studying positive symmetric systems of first order partial differential equations (Friedrichs, 1958),…

We revisit the Krein-von Neumann extension in the case where the underlying symmetric operator is strictly positive and apply this to derive the explicit form of the Krein-von Neumann extension for singular, general (i.e.,…

Given a densely defined skew-symmetric operators A 0 on a real or complex Hilbert space V , we parametrize all m-dissipative extensions in terms of contractions $\Phi$ : H-$\rightarrow$ H + , where Hand H + are Hilbert spaces associated…

Semibounded symmetric operators have a distinguished self-adjoint extension, the Friedrichs extension. The eigenvalues of the Friedrichs extension are given by a variational principle that involves only the domain of the symmetric operator.…

Starting with an adjoint pair of operators, under suitable abstract versions of standard PDE hypotheses, we consider the Weyl M-function of extensions of the operators. The extensions are determined by abstract boundary conditions and we…

Indicial operators are model operators associated to an elliptic differential operator near a corner singularity on a stratified manifold. These model operators are defined on generalized tangent cone configurations and exhibit a natural…

The abstract theory of self-adjoint extensions of symmetric operators is used to construct self-adjoint realizations of a second-order elliptic operator on $\mathbb{R}^{n}$ with linear boundary conditions on (a relatively open part of) a…

We characterize by boundary conditions the Krein-von Neumann extension of a strictly positive minimal operator corresponding to a regular even order quasi-differential expression of Shin-Zettl type. The characterization is stated in terms…

We produce a simple criterion and a constructive recipe to identify those self-adjoint extensions of a lower semi-bounded symmetric operator on Hilbert space which have the same lower bound as the Friedrichs extension. Applications of this…

We consider skew-symmetric operators on a Hilbert space and study m-accretive restrictions of their negative adjoints. Using the theory of boundary systems, we provide a full characterisation of all those m-accretive restrictions, linear…

In this article, we aim to provide a satisfactory algebraic description of the set of affiliated operators for von Neumann algebras. Let $\mathscr{M}$ be a von Neumann algebra acting on a Hilbert space $\mathcal{H}$, and let…

The Krein-von Neumann extension is studied for Schr\"odinger operators on metric graphs. Among other things, its vertex conditions are expressed explicitly, and its relation to other self-adjoint vertex conditions (e.g.…

In this paper, we combine results on extensions of operators with recent results on the relation between the M-function and the spectrum, to examine the spectral behaviour of boundary value problems. M-functions are defined for general…

The problem of connecting the operator parameters that label the same self-adjoint extension of a given symmetric operator, respectively, within the 'absolute' von Neumann extension scheme and the 'relative' boundary-triplet-induced…

We present a new and simple approach to the theory of multiple operator integrals that applies to unbounded operators affiliated with general von Neumann algebras. For semifinite von Neumann algebras we give applications to the Fr\'echet…

Given a densely defined and closed operator $A$ acting on a complex Hilbert space $\mathcal{H}$, we establish a one-to-one correspondence between its closed extensions and subspaces $\mathfrak{M}\subset\mathcal{D}(A^*)$, that are closed…