4 papers
The Adaptive LQ Regulator
Omar Hijab
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 fo…
The Hohenberg-Kohn Theorem for Schrodinger Semigroups
Omar Hijab
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 po…
The Perron-Frobenius Theorem for Markov Semigroups
Omar Hijab
Let , , be the Schrodinger semigroup associated to a potential and Markov semigroup , , on . Existence is established of a left eigenvector and…
Differentiability of functions of matrices
Yury Grabovsky, Omar Hijab, Igor Rivin
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 re…