12 citations · 12 across the 14 of their papers we have counts for
16 papers
Convergence of spectral smoothings from compact quantum group actions
Trevor Camper, Dimitrios Giannakis, Gage Hoefer
In this note, we study complete and quantum Gromov-Hausdorff convergence of operator systems obtained using smoothings of C*-algebras, where our smoothings arise from the action of…
-extreme maps and -homomorphisms from to finite von Neumann algebras
Dimitrios Giannakis, Michael Montgomery, Travis Russell
Given a unital inclusion of -algebras and a unital inclusion into a von Neumann algebra , we invest…
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…
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, $\mathbb…
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…
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…
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…
Learning Dynamical Systems with the Spectral Exterior Calculus
Suddhasattwa Das, Dimitrios Giannakis, Yanbing Gu +1
We present a data-driven framework for learning dynamical systems on compact Riemannian manifolds based on the spectral exterior calculus (SEC). This approach represents vector fie…
Quantum mechanical closure of partial differential equations with symmetries
Chris Vales, David C. Freeman, Joanna Slawinska +1
We develop a statistical framework for the dynamical closure of spatiotemporal dynamics governed by partial differential equations. Employing the mathematical framework of quantum…
Second quantization for classical nonlinear dynamics
Dimitrios Giannakis, Mohammad Javad Latifi Jebelli, Michael Montgomerry +3
Using techniques from many-body quantum theory, we propose a framework for representing the evolution of observables of measure-preserving ergodic flows through infinite-dimensiona…
Physics-informed spectral approximation of Koopman operators
Claire Valva, Dimitrios Giannakis
Koopman operators and transfer operators represent nonlinear dynamics in state space through its induced action on linear spaces of observables and measures, respectively. This fra…
Tensor network approximation of Koopman operators
Dimitrios Giannakis, Mohammad Javad Latifi Jebelli, Michael Montgomery +3
We propose a tensor network framework for approximating the evolution of observables of measure-preserving ergodic systems. Our approach is based on a spectrally-convergent approxi…
Kernel Smoothing Operators on Thick Open Domains
Dimitrios Giannakis, Mohammad Javad Latifi Jebelli
We define the notion of a thick open set in a Euclidean space and show that a local Hardy-Littlewood inequality holds in , . We then establish pointw…
An algebra structure for reproducing kernel Hilbert spaces
Dimitrios Giannakis, Michael Montgomery
Reproducing kernel Hilbert spaces (RKHSs) are Hilbert spaces of functions where pointwise evaluation is continuous. There are known examples of RKHSs that are Banach algebras under…
Consistent spectral approximation of Koopman operators using resolvent compactification
Claire Valva, Dimitrios Giannakis
Koopman operators and transfer operators represent dynamical systems through their induced linear action on vector spaces of observables, enabling the use of operator-theoretic tec…