Dynamical Sampling in Graph Paley--Wiener Spaces
Abstract
We study dynamical sampling for graph signals using the spectral theory of the normalized graph Laplacian. Graph Paley-Wiener spaces GPW_w are defined as spectral subspaces associated with a bandwidth parameter w, and reconstruction is studied from measurements generated by iterates of bounded operators leaving these spaces invariant. For the lattice graph Z, we give an explicit spectral decomposition of the normalized Laplacian, identify the corresponding Graph Paley--Wiener spaces with classical bandlimited spaces on the torus, and recover the classical sampling theorem in this setting. Using frames of operator orbits, we construct dynamical frames for GPW_w(Z) and derive reconstruction formulas. We also discuss the extension to Z^n, where the bandwidth region is described by a sublevel set of the Laplacian symbol. Finally, for finite graphs, we formulate dynamical recovery in GPW_w(G)\) in terms of finite frames generated by iterates of the graph operator. Using the path graph P_N as a numerical model, we study how the number of iterates and the spatial distribution of the sampled vertices affect the optimal frame bounds and the conditioning of the resulting dynamical frame.
Related
- Helson Inequality, Hankel Operators, and Weak Factorization on Paley-Wiener spaces of Convex Domains
- The zeros of point evaluation extremals in Paley-Wiener spaces
- Stochastic Euler Products in the Paley-Wiener Space
- Stability of concentration in the Paley-Wiener space
- A trace Paley-Wiener theorem for GLn(F)backslash GLn(E), with E/F a quadratic extension of non-Archimedean local fields
BibTeX
@misc{bulai2026dynamical,
title = {{Dynamical Sampling in Graph Paley--Wiener Spaces}},
author = {Iulia Martina Bulai and Carlos Cabrelli and Elena Cordero and Ursula Molter and Sandra Saliani},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25472},
eprint = {2609.25472},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25472},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Dynamical Sampling in Graph Paley--Wiener Spaces
AU - Iulia Martina Bulai
AU - Carlos Cabrelli
AU - Elena Cordero
AU - Ursula Molter
AU - Sandra Saliani
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.25472
UR - https://arxiv.org/abs/2609.25472
AB - We study dynamical sampling for graph signals using the spectral theory of the normalized graph Laplacian. Graph Paley-Wiener spaces GPW_w are defined as spectral subspaces associated with a bandwidth parameter w, and reconstruction is studied from measurements generated by iterates of bounded operators leaving these spaces invariant. For the lattice graph Z, we give an explicit spectral decomposition of the normalized Laplacian, identify the corresponding Graph Paley--Wiener spaces with classical bandlimited spaces on the torus, and recover the classical sampling theorem in this setting. Using frames of operator orbits, we construct dynamical frames for GPW_w(Z) and derive reconstruction formulas. We also discuss the extension to Z^n, where the bandwidth region is described by a sublevel set of the Laplacian symbol. Finally, for finite graphs, we formulate dynamical recovery in GPW_w(G)\) in terms of finite frames generated by iterates of the graph operator. Using the path graph P_N as a numerical model, we study how the number of iterates and the spatial distribution of the sampled vertices affect the optimal frame bounds and the conditioning of the resulting dynamical frame.
ER -