Doubly commuting invariant subspaces for representations of product systems of $$C^*$$-correspondences

Wold Decomposition for Representations of Product Systems of C-correspondences

Higher-rank versions of Wold decomposition are shown to hold for doubly commuting isometric representations of product systems of C∗correspondences over N 0 , generalising the classical result for a doubly commuting pair of isometries due to M. S lociński. Certain decompositions are also obtained for the general, not necessarily doubly commuting, case and several corollaries and examples are pr...

Doubly Invariant Subspaces of Annulus Operators

Essential Representations of C-correspondences

Let E be a C∗-correspondence over a C∗-algebraA with non-degenerate faithful left action. We show that E admits sufficiently many essential representations (i.e. representations ψ such that ψ(E)H = H) to recover the Cuntz-Pimsner algebra OE.

Compact representations of Kohn-Sham invariant subspaces.

We present a method to compute a hierarchical approximate representation of the solutions of the Kohn-Sham equations. The method is based on a recursive bisection algorithm and yields one-particle wave functions localized on subdomains of varying sizes. The accuracy of the representation is set a priori by specifying the highest acceptable error in 2-norm for any solution. Applications to large...

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control

In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically co...