A. V. Semenov

collaborators

3 papers

math.FA2025

Universal frame set for rational functions

Andrei V. Semenov

Let $g \in L^{2} (R)$ be a rational function of degree $M$ , i.e., there exist polynomials $P, Q$ such that $g = \frac{P}{Q}$ and $d e g (P) < d e g (Q) \leq M$ . We prove that for a…

math.CV2025

Hereditary completeness for systems of exponentials in weighted $L^{2}$ -spaces

Andrei V. Semenov

We prove that for every $0 < α < 1$ there exists $Λ_{α} \subset R$ such that the system ${e^{iλ t}}_{λ \in Λ_{α}}$ is complete and minimal, but not hereditarily complete in the…

math.CV2023

Frame set for shifted sinc-function

Yurii Belov, Andrei V. Semenov

We prove that frame set $F_{g}$ for imaginary shift of sinc-function $g (t) = \frac{sin π b ( t - i w )}{t - i w}, b, w \in R ∖ {0}$ can be described as $\mathcal{…

Universal frame set for rational functions

Hereditary completeness for systems of exponentials in weighted L2-spaces

Frame set for shifted sinc-function

Hereditary completeness for systems of exponentials in weighted $L^{2}$ -spaces