Boosting the van der Corput inequality using the tensor power trick

In this previous blog post I noted the following easy application of Cauchy-Schwarz: Lemma 1 (Van der Corput inequality) Let be unit vectors in a Hilbert space . Then Proof: The left-hand side may be written as for some unit complex numbers . By Cauchy-Schwarz we have and the claim now follows from the triangle […]