Uploaded April 2021 | Updated September 2026, 1 day ago

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In this video we show how we can exploit the linearity in the symbol of Liouville operators to define an inner product on dynamical systems that give rise to densely defined Liouville operators over a reproducing kernel Hilbert space (RKHS).

Music:
Come 2gether by Ooyy
Video Call from Los Angeles by Trevor Kowalski
Wrong by Dan Henig
Guardians + Tek by Craig Hardgrove

0:00 Intro and Clip
0:32 Opening Remarks
0:54 Why Inner Products
5:59 Adjoints for Inner Products
7:44 Errata Heads Up
9:25 Inner Products on Dynamical Systems
10:44 Computing Trajectories
20:18 Inner Products from Pre Inner Products
26:37 Closing Remarks