5 problems

Fourier and Parseval subspace conjecture. If $\{\chi_{\alpha}\}_{\alpha\in A}$ is complete, then

Let $G$ be a connected, simply connected nilpotent Lie group and let $(\pi,\mathcal{H})$ be an irreducible unitary representation of $G$ that is square-integrable modulo the center…

Let $\mathcal H$ be the Hilbert space under consideration, and let $\mathcal F_{\hat e}=\{\hat e_n\}$ be the orthonormal set obtained from the positive square roots of the operator…

Completeness of CPWs. There exists a constant $\mu_0$ such that the set $\{\mathrm{b}^n_{\mathbf{j}}\}_{n,\mathbf{j}}$ generated from the recursive variational definitions is compl…

Let $d\mu_k$ be normalized Haar measure on $U(k)$, and let ${\mathbb E}_k$ denote expectation with respect to this measure. Let $\Lambda_k$ denote the quantity measuring the aggreg…