Related papers: Self-adjointness of a simplified Dirac interaction…
This paper addresses two different but related questions regarding an unbounded symmetric tridiagonal operator: its self-adjointness and the approximation of its spectrum by the eigenvalues of its finite truncations. The sufficient…
Given a self-adjoint involution J on a Hilbert space H, we consider a J-self-adjoint operator L=A+V on H where A is a possibly unbounded self-adjoint operator commuting with J and V a bounded J-self-adjoint operator anti-commuting with J.…
We present a new method to transform an expanded class of non-selfadjoint advection-diffusion operators into self-adjoint operators. The transform is based on a combination of a point transform and Lie transform in conjunction with an…
Formally symmetric differential operators on weighted Hardy-Hilbert spaces are analyzed, along with adjoint pairs of differential operators. Eigenvalue problems for such operators are rather special, but include many of the classical…
Given a self-adjoint operator $T$ on a separable infinite-dimensional Hilbert space we study the problem of characterizing the set $\mathcal D(T)$ of all possible diagonals of $T$. For operators $T$ with at least two points in their…
In this paper spectral theorems for not necessarily continuous normal and self-adjoint random operators on a complex separable Hilbert space are proved.
We prove a general theorem about the self-adjointness and domain of Pauli-Fierz type Hamiltonians. Our proof is based on commutator arguments which allow us to treat fields with non-commuting components. As a corollary it follows that the…
This paper is devoted to the construction of what we will call {\em exactly solvable models}, i.e. of quantum mechanical systems described by an Hamiltonian $H$ whose eigenvalues and eigenvectors can be explicitly constructed out of some…
General point interactions for the second derivative operator in one dimension are studied. In particular, ${\mathcal P \mathcal T}$-self-adjoint point interactions with the support at the origin and at points $\pm l$ are considered. The…
We characterise the Kato property of a sectorial form $\mathfrak{a}$, defined on a Hilbert space $V$, with respect to a larger Hilbert space $H$ in terms of two bounded, selfadjoint operators $T$ and $Q$ determined by the imaginary part of…
The quantization of closed cosmologies makes it necessary to study squared Dirac operators on closed intervals and the corresponding quantum amplitudes. This paper proves self-adjointness of these second-order elliptic operators.
Let $U$ be an operator in a Hilbert space $\mathcal{H}_{0}$, and let $\mathcal{K}\subset\mathcal{H}_{0}$ be a closed and invariant subspace. Suppose there is a period-2 unitary operator $J$ in $\mathcal{H}_{0}$ such that $JUJ=U^*$, and $PJP…
We study self-adjoint extensions of operators which are the product of the multiplication operator by an analytic function and the analytic continuation in a strip. We compute the deficiency indices of the product operator for a wide class…
In this note we prove that the maximally defined operator associated with a class of Dirac-type differential expressions M(Q) is J-self-adjoint with respect to a proper antilinear conjugation J under the general hypothesis that the entries…
We develop a mathematical concept towards gauge field theories based upon a Hilbert space endowed with a representation of a skew-adjoint Lie algebra and an action of a generalized Dirac operator. This concept shares common features with…
Given a self-adjoint operator $T$ on a separable infinite-dimensional Hilbert space we study the problem of characterizing the set $\mathcal D(T)$ of all possible diagonals of $T$. For compact operators $T$, we give a complete…
The eigenvalues of a self-adjoint nxn matrix A can be put into a decreasing sequence $\lambda=(\lambda_1,...,\lambda_n)$, with repetitions according to multiplicity, and the diagonal of A is a point of $R^n$ that bears some relation to…
We consider a two-dimensional massless Dirac operator coupled to a magnetic field $B$ and an electric potential $V$ growing at infinity. We find a characterization of the spectrum of the resulting operator $H$ in terms of the relation…
This note deals with the operator $T^*T$, where $T$ is a densely defined operator on a complex Hilbert space. We reprove a recent result of Z. Sebesty\'en and Zs. Tarcsay [13]: If $T^*T$ and $TT^*$ are self-adjoint, then $T$ is closed. In…
Low-energy scattering is well described by the effective-range expansion. In quantum mechanics, a tower of contact interactions can generate terms in this expansion after renormalization. Scattering parameters are also encoded in the…