I shall prove the so-called outer kernel theorem for bounded linear operators mapping the co-orbit space of test functions induced by a localised frame for a Hilbert space on the co-orbit space of distributions induced by a localised frame for another Hilbert space. The proof of the theorem relies on using Galerkin’s method to transform any given operator into a matrix, before synthesising the kernel of the operator from the matrix.
https://univienna.zoom.us/j/62077153839?pwd=T3pxeHNRNEU0RlFoY1J2cnIzbzU5dz09