Mathématiques > Accueil > Avancées en Mathématiques Pures et Appliquées > Numéro
In this paper, we study frame properties of finite sums of frames from the Weyl-Heisenberg group. We give sufficient conditions for a finite sum of frames of the space $$$L^2(\mathbb{R})$$$ from the Weyl-Heisenberg group, with explicit frame bounds, to be a frame for $$$L^2(\mathbb{R})$$$. These conditions are given in terms of frame bounds and scalars involved in the finite sum of frames. We show that the sum of a frame from the Weyl-Heisenberg group and its dual frame always constitutes a frame. Further, we provide sufficient conditions for the sum of images of frames under bounded linear operators acting on $$$L^2(\mathbb{R})$$$ to be a frame. These are expressed in terms of the lower bounds of their Hilbert-adjoint operator. We also discuss finite sums of frames where the frames are perturbed by bounded sequences of scalars. As an application, we show that the frame bounds of sums of frames can increase the rate of approximation in the frame algorithm.
We develop topological partitions for m-to-1 local homeomorphisms on compact metric spaces—maps that arise naturally in non-invertible dynamical systems, such as expanding and covering maps. These partitions enable a symbolic representation of the dynamics via the zip shift, an extended bilateral shift in the non-invertible setting. Inspired by Smale’s horseshoe construction, this approach generalizes topological partitions to a broader class of systems and opens new directions for studying their topological and ergodic properties.
This paper presents a necessary and sufficient condition for a topological vector group to be locally compact. We also introduce several sufficient conditions that ensure the local compactness of topological vector groups. Furthermore, we establish a sufficient condition for a topological vector group to be first countable.
2026
Volume 26- 17
Numéro 1 (Janvier 2026)2025
Volume 25- 16
Numéro 1 (Janvier 2025)2024
Volume 24- 15
Numéro 1 (Janvier 2024)2023
Volume 23- 14
Numéro 1 (Janvier 2023)2022
Volume 22- 13
Numéro 1 (Janvier 2022)2021
Volume 21- 12
Numéro spécial : AUS-ICMS 20202020
Volume 20- 11
Numéro 1 (Mai 2020)