Outer Kernel Theorem for Co-orbit Spaces of Localised Frames

Dimitri Bytchenkoff, Michael Speckbacher, Peter Balazs

Abstract: We prove a so-called outer kernel theorem for bounded linear operators between co-orbit spaces generated from a localised frame $\Psi$. In particular, we show that there is a bijective correspondence between the bounded linear operators mapping the co-orbit space of test functions $H^1_w(\Psi)}$ to the co-orbit space of distributions $H^\infty_{1/w}(\Psi)}$ and their kernels in $H^\{infty, \otimes}_{1/w}(\Psi)}$. The proof of the theorem relies on general properties of localised frames, tensor products and Galerkin's method for matrix represention of operators.

Submission Type: Full Paper