Related papers: Lame operators with projective octahedral and icos…

Let $n\in\mathbb{N}$ and let $A$ be a closed linear operator (everywhere bounded or unbounded). In this paper, we study (among others) equations of the type $A^*A=A^n$ where $n\geq2$ and see when they yield $A=A^*$ (or a weaker class of…

Given an idempotent operator $E$ in a complex Hilbert space ${\mathcal H}$, one can associate to it two orthogonal projections: - The polar decomposition $2E-1=(2P-1)|2E-1|$ provides an orthogonal projection $P$. That the unitary part in…

We introduce a new category of differential graded multi-oriented props whose representations (called homotopy algebras with branes) in a graded vector space require a choice of a collection of $k$ linear subspaces in that space, $k$ being…

The observation that $n$ pairs of para-Bose (pB) operators generate the universal enveloping algebra of the orthosymplectic Lie superalgebra $osp(1/2n)$ is used in order to define deformed pB operators. It is shown that these operators are…

The 2:1 two-dimensional anisotropic quantum harmonic oscillator is considered and new sets of states are defined by means of normal-ordering non-linear operators through the use of non-commutative binomial theorems as well as solving…

We recall results concerning one-dimensional classical and quantum systems with ladder operators. We obtain the most general one-dimensional classical systems respectively with a third and a fourth order ladder operators satisfying…

We introduce inner band projections in the space of regular operators on a Dedekind complete Banach lattice and study some structural properties of this class. In particular, we provide a new characterization of atomic order continuous…

Averaged operators are important in Convex Analysis and Optimization Algorithms. In this paper, we propose classifications of averaged operators, firmly nonexpansive operators, and proximal operators using the Bauschke-Bendit-Moursi modulus…

Trigonometric formulas are derived for certain families of associated Legendre functions of fractional degree and order, for use in approximation theory. These functions are algebraic, and when viewed as Gauss hypergeometric functions,…

We construct new examples of free curve arrangements in the complex projective plane using point-line operators recently defined by the second author. In particular, we construct a new example of a conic-line arrangement with ordinary…

Motivated by the finite-gap structure of the classical Lam\'{e} equation (1.2) and its central role in mathematical physics, generalized Lam\'{e}-type equations (1.12) are investigated. For the fundamental case $n=1$, a monodromy…

In this paper, we obtain a new class of functions, which is developed via the Hermite--Hadamard inequality for convex functions. The well-known one-one correspondence between the class of operator monotone functions and operator connections…

We give a simple geometric characterization of isospectral orbifolds covered by spheres, complex projective spaces and the quaternion projective line having cyclic fundamental group. The differential operators considered are…

We study Lam\'e operators of the form $$L = -\frac{d^2}{dx^2} + m(m+1)\omega^2\wp(\omega x+z_0),$$ with $m\in\mathbb{N}$ and $\omega$ a half-period of $\wp(z)$. For rectangular period lattices, we can choose $\omega$ and $z_0$ such that the…

A plane tiling consisting of congruent copies of a shape is isohedral provided that for any pair of copies, there exists a symmetry of the tiling mapping one copy to the other. We give a $O(n\log^2{n})$-time algorithm for deciding if a…

Projection operators arise naturally as one-particle density operators associated to Slater determinants in fields such as quantum mechanics and the study of determinantal processes. In the context of the semiclassical approximation of…

Let $X$ be a finite-dimensional normed space and let $Y \subseteq X$ be its proper linear subspace. The set of all minimal projections from $X$ to $Y$ is a convex subset of the space all linear operators from $X$ to $X$ and we can consider…

Given a complemented poset P, we can assign to every element x of P the set x^+ of all its complements. We study properties of the operator ^+ on P, in particular, we are interested in the case when x^+ forms an antichain or when ^+ is…

We introduce and study the notion of orthosymmetric spaces over an Archimedean vector lattice as a generalization of finite-dimentional Euclidean inner spaces. A special attention has been paid to linear operators on these spaces.

For the algebra $\mI_1= K<x, \frac{d}{dx}, \int>$ of polynomial integro-differential operators over a field $K$ of characteristic zero, a classification of simple modules is given. It is proved that $\mI_1$ is a left and right coherent…