Related papers: Self-Adjointness of Deformed Unbounded Operators

Negative-index metamaterials possess a negative refractive index and thus present an interesting substance for designing uncommon optical effects such as invisibility cloaking. This paper deals with operators encountered in an…

We study generic fractal properties of bounded self-adjoint operators through lower and upper generalized fractal dimensions of their spectral measures. Two groups of results are presented. Firstly, it is shown that the set of vectors whose…

We construct operators which factorize the transfer function associated with a non-self-adjoint 2x2 operator matrix whose diagonal entries can have overlapping spectra and whose off-diagonal entries are unbounded operators.

Assume that $T$ is a self-adjoint operator on a Hilbert space $\mathcal{H}$ and that the spectrum of $T$ is confined in the union $\bigcup_{j\in J}\Delta_j$, $J\subseteq\mathbb{Z}$, of segments $\Delta_j=[\alpha_j,…

We study maximal representations of nonnegative sesquilinear forms in real or complex Hilbert spaces, that are not necessarily closed or even closable. We associate positive self-adjoint operators with such forms, in a sense similar to…

We prove that the curved Ovsienko--Redou operators and a related family of differential operators are formally self-adjoint. This verifies two conjectures of Case, Lin, and Yuan.

Let $T$ be a self-adjoint operator in a Hilbert space $H$ with domain $\mathcal D(T)$. Assume that the spectrum of $T$ is confined in the union of disjoint intervals $\Delta_k =[\alpha_{2k-1},\alpha_{2k}]$, $k\in \mathbb{Z}$, and $$…

We consider Schr\"odinger operators on possibly noncompact Riemannian manifolds, acting on sections in vector bundles, with locally square integrable potentials whose negative part is in the underlying Kato class. Using path integral…

We consider a one-parameter family of degenerately elliptic operators $\cal{L}_\gamma$ on the closed disk $\mathbb{D}$, of Keldysh (or Kimura) type, which appears in prior work [Mishra et al., Inverse Problems (2022)] by the authors and…

In this article, we conduct a study of integral operators defined in terms of non-convolution type kernels with singularities of various degrees. The operators that fall within our scope of research include fractional integrals, fractional…

We expand on some invariants used for classifying nonselfadjoint operator algebras. Specifically to nonselfadjoint operator algebras which have a conditional expectation onto a commutative diagonal we construct an edge-colored directed…

In this notes unbounded regular operators on Hilbert $C^*$-modules over arbitrary $C^*$-algebras are discussed. A densely defined operator $t$ possesses an adjoint operator if the graph of $t$ is an orthogonal summand. Moreover, for a…

In this paper, necessary and sufficient conditions are established for the factorization of a closed, in general, unbounded operator $T=AB$ into a product of two nonnegative selfadjoint operators $A$ and $B.$ Already the special case, where…

We use boundary triples to find a parametrization of all self-adjoint extensions of the magnetic Schr\"odinger operator, in a quasi-convex domain~$\Omega$ with compact boundary, and magnetic potentials with components in…

We prove that if $0<\a<1$ and $f$ is in the H\"older class $\L_\a(\R)$, then for arbitrary self-adjoint operators $A$ and $B$ with bounded $A-B$, the operator $f(A)-f(B)$ is bounded and $\|f(A)-f(B)\|\le\const\|A-B\|^\a$. We prove a similar…

This paper is devoted to the study of essential self-adjointness of a relativistic Schr\"{o}dinger operator with a singular homogeneous potential. From an explicit condition on the coefficient of the singular term, we provide a sufficient…

We show that all self-adjoint extensions of semi-bounded Sturm--Liouville operators with general limit-circle endpoint(s) can be obtained via an additive singular form bounded self-adjoint perturbation of rank equal to the deficiency…

We consider selfadjoint operators obtained by pasting a finite number of boundary relations with one-dimensional boundary space. A typical example of such an operator is the Schr\"odinger operator on a star-graph with a finite number of…

In noncommutative geometry one is interested in invariants such as the Fredholm index or spectral flow and their calculation using cyclic cocycles. A variety of formulae have been established under side conditions called summability…

An adjoint pair is a pair of densely defined linear operators $A, B$ on a Hilbert space such that $\langle Ax,y\rangle=\langle x,By\rangle$ for $x\in \cD(A), y \in \cD(B).$ We consider adjoint pairs for which $0$ is a regular point for both…