11 papers
Measure-free Koopman-von Neumann Dynamics and Noncommutative Geometry
Dimitrios Giannakis, Michael Montgomery
The Koopman-von Neumann formulation of classical statistical dynamics maps the isometric evolution of probability densities in under the Liouville equation to a unitary evolu…
Affiliated operators for classical and quantum control
Dimitrios Giannakis, Gage Hoefer
Using techniques from the theory of von Neumann algebras, we propose a framework for addressing questions of controllability of bilinear systems on infinite dimensional Hilbert spa…
Accelerated decomposition of bistochastic kernel matrices by low rank approximation
Chris Vales, Dimitrios Giannakis
We develop an accelerated algorithm for the approximate eigenvalue decomposition of symmetrically normalized kernel matrices, focusing on a bistochastic normalization. Our approach…
Data-driven methods for computation of optimal linear response in high-dimensional dynamical systems
Gary Froyland, Dimitrios Giannakis, Nicholas Peters
We develop a data-driven framework for estimating optimal linear response of nonlinear dynamical systems. Our approach is based on kernel-smoothed approximations of the transfer/Ko…
On Algebras of Functions over Infinite Dimensions
Dimitrios Giannakis, Mohammad Javad Latifi Jebelli, Michael Montgomery
We introduce a family of reproducing kernel Hilbert spaces of holomorphic functions defined on an infinite--dimensional domain in a separable Hilbert space, $\mathb…
Koopman and transfer operator techniques from the perspective of quantum theory
Dimitrios Giannakis, Michael Montgomery
The study of mathematical connections between operator-theoretic formulations of classical dynamics and quantum mechanics began at least as early as the 1930s in work of Koopman an…