arXiv subjects

Omar Hijab

Publications and source records attributed to Omar Hijab.

4 recordsLinked to original sources

arXiv2019

The Adaptive LQ Regulator

The optimal adaptive control of a linear system in a signal-plus-noise setting with infinite horizon LQ regulator cost is studied. The class of partially observed linear systems for which the certainty equivalence property holds is identified. It is also shown that a linear system is adaptively stabilizable if and only if it is uniformly stabilizable, and the class of partially observed linear systems for which the certainty equivalence value function is a supersolution of the Bellman equation is identified.

math.OC↗

arXiv2017

The Hohenberg-Kohn Theorem for Schrodinger Semigroups

At the basis of much of computational chemistry is density functional theory, as initiated by the Hohenberg-Kohn theorem. The theorem states that, when nuclei are fixed, nuclear potentials are determined by $1$-electron densities. We recast and derive this result within the context of the principal eigenvalue of Schrodinger semigroups.

math.FA↗

arXiv2014

The Perron-Frobenius Theorem for Markov Semigroups

Let $P^V_t$, $t\ge0$, be the Schrodinger semigroup associated to a potential $V$ and Markov semigroup $P_t$, $t\ge0$, on $C(X)$. Existence is established of a left eigenvector and right eigenvector corresponding to the spectral radius $e^{λ_0t}$ of $P^V_t$, simultaneously for all $t\ge0$. This is derived with no compactness assumption on the semigroup operators.

math.FA↗

arXiv2003

Differentiability of functions of matrices

Given a function on diagonal matrices, there is a unique way to extend this to an invariant (by conjugation) function on symmetric matrices. We show that the extension preserves regularity -- that is, if the original function is k times differentiable so is the extension (likewise for analyticity and the class k+alpha).

math.FA↗