Abstract In this talk, I will discuss several new results on non-concentration of Neumann eigenfunctions in shrinking neighborhoods of planar domains. The main result is a sharp estimate in a neighborhood of a corner point, but I will also discuss some other results in smoother situations. The main tools are a Rellich commutator argument and an induction argument to control boundary error terms...
AbstractWe introduce an quantum entropy for bimodule quantum channels on finite von Neumann algebras, generalizing the remarkable Pimsner-Popa entropy. The relative entropy for Fourier multipliers of bimodule quantum channels establishes an upper bound of the quantum entropy. Additionally, we present the Araki relative entropy for bimodule quantum channels, revealing its equivalence to the rela...