Related papers: Infinite Dimensional Orthogonal Preserving Quadrat…
This article gives a summary of the finite-dimesional irreducible representations of the $q$-Onsager algebra, which are treated in detail in our paper `The augmented tridiagonal algebra'.
We introduce a notion of ``hereditarily antisymmetric'' operator algebras and prove a structure theorem for them in finite dimensions. We also characterize those operator algebras in finite dimensions which can be made upper triangular and…
In this paper, we introduce a quadratic stochastic operators on the set of all probability measures of a measurable space. We study the dynamics of the Lebesgue quadratic stochastic operator on the set of all Lebesgue measures of the set…
In this paper, the problem of finite horizon inverse optimal control (IOC) is investigated, where the quadratic cost function of a dynamic process is required to be recovered based on the observation of optimal control sequences. We propose…
In the present paper we introduce a concept of doubly stochastic quadratic operator. We prove necessary and sufficient conditions for doubly stochasticity of operator. Besides, we prove that the set of all doubly stochastic operators forms…
We derive orthogonality relations for discrete q-ultraspherical polynomials and their duals by means of operators of representations of the quantum algebra su_q(1,1). Spectra and eigenfunctions of these operators are found explicitly. These…
Quadratic harnesses are time-inhomogeneous Markov polynomial processes with linear conditional expectations and quadratic conditional variances with respect to the past-future filtrations. Typically they are determined by five numerical…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. The associated special functions are eigenfunctions of some shape invariant operators. These operators can…
Infinite order differential operators appear in different fields of Mathematics and Physics and in the last decades they turned out to be of fundamental importance in the study of the evolution of superoscillations as initial datum for…
We numerically study the crossing symmetry constraints in 4D CFTs, using previously introduced algorithms based on semidefinite programming. We study bounds on OPE coefficients of tensor operators as a function of their scaling dimension…
We study mapping properties of the averaging operator related to the variety $ V={x\in \mathbb F_q^d: Q(x)=0},$ where $Q(x)$ is a nondegenerate quadratic polynomial over a finite field $\mathbb F_q$ with $q$ elements. This paper is devoted…
We study approximately orthogonality (in the sense of Dragomir) preserving and reversing operators. We show that for some orthogonality notations, an operator defined from a finite-dimensional Banach space to a normed linear space is…
We study the dissipativity of linear infinite-dimensional systems with respect to a prescribed quadratic supply rate functional. We characterize this property via an operator inequality that also yields the system's dissipation rate. We…
The Heisenberg Oscillator Algebra admits irreducible representations both on the ring $B$ of polynomials in infinitely many indeterminates (the {\em bosonic representation}) and on a graded-by-{\em charge} vector space, the {\em…
A sequential quadratic optimization algorithm for minimizing an objective function defined by an expectation subject to nonlinear inequality and equality constraints is proposed, analyzed, and tested. The context of interest is when it is…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
We prove existence and uniqueness of the mild solution of an infinite dimensional, operator valued, backward stochastic Riccati equation. We exploit the regularizing properties of the semigroup generated by the unbounded operator involved…
The existence of conservative quasipolynomial (QP) maps is investigated. A classification is given for dimensions two and three, and the analytical solution of the former case is constructed. General properties of n-dimensional QP…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
The properties of continued fractions whose partial quotients belong to a quadratic number field K are distinct from those of classical continued fractions. Unlike classical continued fractions, it is currently impossible to identify…