10 problems

Let ${\cal H}$ be a Hilbert space, let $\Phi=(\varphi_n)$ and $\Psi=(\psi_n)$ be sequences in ${\cal H}$, and let $m=(m_n)$ be a complex sequence. The multiplier $M_{m,\Phi,\Psi}$…

Let $H$ be a Hilbert space, let $T_1,T_2\in B(H)$ commute, and suppose that $\\{T_1^iT_2^j\varphi\\}_{i,j\geq 0}$ is an overcomplete frame for $H$. Let $R_1$ and $R_2$ be the assoc…

Strong-frame conjecture. Every $\mathfrak s$-frame for $\mathcal S$ induced by a pair of sequences as in Theorem 2 of KNS is a strong frame.

Let $(\Omega,\mu)$ and $(\Delta,\nu)$ be measure spaces, let $\mathcal{H}$ be a Hilbert space, and let $\{\tau_\alpha\}_{\alpha\in\Omega}$ and $\{\omega_\beta\}_{\beta\in\Delta}$ b…

The unilateral frame number conjecture.

Fourier completeness criterion. The Fourier frequencies $\{e_n\}_{n\in\mathbb{N}_0^d}$ are total in $L^2(\mu)$ if and only if $v$ is non-constant, namely, not proportional to…

Normal-reductive extension conjecture. Theorem remains true if $A$ is a normal reductive operator.

Normalized-frame conjecture. The system above is not a frame for $\mathcal{H}$.

Atomicity conjecture. If $R(\Phi)<\infty$, then $(X,\mu)$ is atomic.

Let $A$ be an invertible matrix, let $\Gamma$ be a lattice in $\mathbb{R}^n$, let $B=A^T$, and let $\Psi=\\{\psi_1,\dots,\psi_L\\}$ generate the wavelet system…