On an analogy between the Wiener--Hopf formulations of discrete and continuous diffraction problems
Mathematical Physics
2025-07-08 v1 Analysis of PDEs
Complex Variables
math.MP
Abstract
This article is dedicated to unifying the framework used to derive the Wiener--Hopf equations arising from some discrete and continuous wave diffraction problems.The main tools are the discrete Green's identity and the appropriate notion of discrete normal derivative. The resulting formal analogy between the Wiener--Hopf equations allows one to effortlessly move between the discrete and continuous formulations. The validity of this novel analogy is illustrated through several famous two-dimensional canonical diffraction problems and extended to three-dimensional problems.
Keywords
Cite
@article{arxiv.2507.04979,
title = {On an analogy between the Wiener--Hopf formulations of discrete and continuous diffraction problems},
author = {A. I. Korolkov and R. C. Assier and A. V. Kisil},
journal= {arXiv preprint arXiv:2507.04979},
year = {2025}
}