Related papers: Local numerical range for a class of $2\otimes d$ …
In this paper, we generalize the notion of the $C$-numerical range of a matrix to operators in arbitrary tracial von Neumann algebras. For each self-adjoint operator $C$, the $C$-numerical range of such an operator is defined; it is a…
We study containment regions of the numerical range of the product of operators $A$ and $B$ such that $W(A)$ and $W(B)$ are line segments. It is shown that the containment region is equal to the convex hull of elliptical disks determined by…
Numerical range of a Hermitian operator X is defined as the set of all possible expectation values of this observable among a normalized quantum state. We analyze a modification of this definition in which the expectation value is taken…
We show that 2D periodic operators with local and perpendicular defects form an algebra. We provide an algorithm of finding spectrum for such operators. While the continuous spectral components can be computed by simple algebraic operations…
We prove new enclosures for the spectrum of non-selfadjoint operator matrices associated with second order linear differential equations $\ddot{z}(t) + D \dot{z} (t) + A_0 z(t) = 0$ in a Hilbert space. Our main tool is the quadratic…
We determine all Hermitian $\mathcal{O}_{\Q(\sqrt{d})}$-matrices for which every eigenvalue is in the interval [-2,2], for each d in {-2,-7,-11,-15\}. To do so, we generalise charged signed graphs to $\mathcal{L}$-graphs for appropriate…
Let $D\subset R^d$ be a bounded domain and let \[ L=\frac12\nabla\cdot a\nabla +b\cdot\nabla \] %\[ %L=\frac12\sum_{i,j=1}^da_{i,j}\frac{\partial^2}{\partial x_i\partial x_j}+\sum_{i=1}^db_i\frac{\partial}{\partial x_i}, %\] be a second…
In dynamical systems such as cellular automata and iterated maps, it is often useful to look at a language or set of symbol sequences produced by the system. There are well-established classification schemes, such as the Chomsky hierarchy,…
Let $\mathcal{O} \subset \mathbb{R}^d$ be a bounded domain of class $C^2$. In the Hilbert space $L_2(\mathcal{O};\mathbb{C}^n)$, we consider a matrix elliptic second order differential operator $\mathcal{A}_{D,\varepsilon}$ with the…
It is known that a real symmetric circulant matrix with diagonal entries $d\geq0$, off-diagonal entries $\pm1$ and orthogonal rows exists only of order $2d+2$ (and trivially of order $1$) [Turek and Goyeneche 2019]. In this paper we…
$L$-ensembles are a class of determinantal point processes which can be viewed as a statistical mechanical systems in the grand canonical ensemble. Circulant $L$-ensembles are the subclass which are locally translationally invariant and…
We generalise the Elliptical Range Theorem to characterise the numerical range of matrices belonging to a subspace of the space of \(3 \times 3\) matrices. Using Specht's Theorem, which characterizes when two matrices are unitarily…
In this paper we first construct an analytic realization of the $C_\lambda$-extended oscillator algebra with the help of difference-differential operators. Secondly, we study families of $d$-orthogonal polynomials which are extensions of…
Several upper and lower bounds for the numerical radius of $2 \times 2$ operator matrices are developed which refine and generalize the earlier related bounds. In particular, we show that if $B,C$ are bounded linear operators on a complex…
An analysis of the boundary representations and C$^*$-envelopes of some finite-dimensional operator systems $\mathcal R$ is undertaken by considering relationships between operator-theoretic properties of a $d$-tuple $\mathfrak…
We consider linear and obstacle problems driven by a nonlocal integral operator, for which nonlocal interactions are restricted to a ball of finite radius. These type of operators are used to model anomalous diffusion and, for a special…
The quadratic numerical range $W^2(A)$ is a subset of the standard numerical range of a linear operator which still contains its spectrum. It arises naturally in operators which have a $2 \times 2$ block structure, and it consists of at…
In this paper we introduce an enclosure of the numerical range of a class of rational operator functions. In contrast to the numerical range the presented enclosure can be computed exactly in the infinite dimensional case as well as in the…
In this paper, we define a new concept of numerical range $W_{o}(\cdot)$ and prove its basic results. We also define the numerical radius $\omega_{o}(\cdot)$ and prove that $$\omega_{o}(T)\leq||| T|||\leq 2\omega_{o}(T).$$
We study orthogonal and symplectic matrix models with polynomial potentials and multi interval supports of the equilibrium measure. For these models we find the bounds (similar to the case of hermitian matrix models) for the rate of…