3 problems

Let $\zeta_1,\dots,\zeta_d\in\mathbb{C}$ be the spectral points used in the finite-dimensional Orthomin analysis, and let $\operatorname{Hull}(\zeta_1,\dots,\zeta_d)$ denote their…

Let $\mathbb{S}^1$ be the unit circle with Haar probability measure $d\mu_0$, and let $U:L^2(\mathbb{S}^1,d\mu_0)\to L^2(\mathbb{S}^1,d\mu_0)$ be the multiplication operator … Cons…

Let $k\in\mathbb{N}$. For each $d\in\mathbb{N}$, let $U=\operatorname{diag}(1,\zeta_d,\zeta_d^2,\dots,\zeta_d^{d-1})$, where $\zeta_d=\exp(2\pi \mathbf{i}/d)$ is a primitive root o…