April 18, 2024
Our paper entitled The mystery of Carleson frames has just been accepted for publication in Applied Computational and Harmonic Analysis. The paper is about thinnings of Carleson frames - frames generated by powers of a normal operator, which were found and characterized by Aldroubi et al.
Coauthors: Ole Christensen (DTU Copenhagen), Marzieh Hasannasab (DTU Copenhagen), Diana Stoeva (Uni Vienna)
April 9, 2024
I am happy and feel honored to be a speaker at the Fourth Symposium on Machine Learning and Dynamical Systems which will take place at the Fields Institute of Toronto, July 8-12, 2024, and is organized by Boumediene Hamzi.
April 1, 2024
Our paper Error bounds for kernel-based approximations of the Koopman operator just got accepted for publication in Applied Computational and Harmonic Analysis. In this work, we analyze kernel-based EDMD for stochastic differential equations and prove finite-data error bounds in the L²-norm.
Coauthors: Manuel Schaller (TU Ilmenau), Karl Worthmann (TU Ilmenau), Sebastian Peitz (Uni Paderborn), and Feliks Nüske (MPI Magdeburg and HU Berlin)
March 27, 2024
We have just published our latest preprint L∞-error bounds for approximations of the Koopman operator by kernel extended dynamic mode decomposition on the arXiv. In this paper, we exploit the fact that regression in RKHSs can be recast as interpolation to derive the first pointwise error bounds on the kEDMD approximant of the Koopman operator in the literature.
Coauthors: Frederik Köhne (Uni Bayreuth), Anton Schiela (Uni Bayreuth), Manuel Schaller (TU Ilmenau), and Karl Worthmann (TU Ilmenau)