2 problems

Let ${\cal H}$ be a Hilbert space. A sequence $(f_n)$ in ${\cal H}$ is a weighted frame when there exists $(\omega_n)\subset(0,+\infty)$ such that $(\omega_n f_n)$ is a frame for…

Let ${\cal H}$ be a Hilbert space, let $(f_n)$ be a complete sequence in ${\cal H}$, and let $A\in(0,\infty)$. A sequence is a lower semi frame for ${\cal H}$ with bound $A$ when i…