6 papers
The role of parameter Jacobians in the stability of network outputs
Halyun Jeong, Palle E. T. Jorgensen, Hyun-Kyoung Kwon +2
In the framework of network dynamics, learning models, and neural tangent kernels (NTK), we show that the corresponding linearized dynamics leads naturally to a semigroup formulati…
Scattering map for the Vlasov--Poisson system with a repulsive harmonic potential
Wenrui Huang, Hyunwoo Kwon
We consider the Vlasov--Poisson system with a repulsive harmonic potential and prove (modified) scattering of solutions for small initial data. Moreover, we construct (modified) wa…
Infinite-Dimensional Operator/Block Kaczmarz Algorithms: Regret Bounds and -Effectiveness
Halyun Jeong, Palle E. T. Jorgensen, Hyun-Kyoung Kwon +1
We present a variety of projection-based linear regression algorithms with a focus on modern machine-learning models and their algorithmic performance. We study the role of the rel…
Decay estimates for Schrödinger's equation with magnetic potentials in three dimensions
Marius Beceanu, Hyun-Kyoung Kwon
In this paper we prove that Schrödinger's equation with a Hamiltonian of the form , which includes a magnetic potential , has the same dispersiv…
On the metric of the jet bundle and similarity of Cowen-Douglas operators
Kui Ji, Shanshan Ji, Hyun-Kyoung Kwon +1
The study of Cowen-Douglas operators not only involves traditional operator-theoretic tools but also concepts and results from complex geometry on holomorphic vector bundles. We ma…
The Eigenvalue Problem for the Laplacian via Conformal Mapping and the Gohberg--Sigal Theory
Marius Beceanu, Jiho Hong, Hyun-Kyoung Kwon +1
We consider the Dirichlet and Neumann eigenvalues of the Laplacian for a planar, simply connected domain. The eigenvalues admit a characterization in terms of a layer potential of…