Seminars

We define a nonlinear Fourier transform which maps sequences of contractive $n \times n$ matrices to $SU(2n)$-valued functions on the circle $\mathbb T$. We characterize the image of compactly supported sequences and square-summable sequences on the half-line, and prove that the inverse map is well-defined on $SU(2n)$-valued functions whose diagonal $n \times n$ blocks are outer matrix functions. As an application, we prove infinite generalized quantum signal processing in the fully coherent regime.