Summary
International Symposium on Antennas and Propagation
2008
Session Number:1IS01A
Session:
Number:1IS01A-3
Modern Mathematics in Antenna Arrays
Hiroaki MIYASHITA, Yoshihiko KONISHI,
pp.-
Publication Date:2008/10/27
Online ISSN:2188-5079
Summary:
Recent remarkable developments in mathematical physics are encouraged by borderless interactions between pure mathematics and physics. For example, even in ‘pure’ classical physics such as mechanics is much influenced by analyses on manifolds including differential geometry and topology[1]. There, one of the central concepts is the Lagrangian submanifolds, and it even found a way in asymptotic analyses of the wave phenomena such as the Maslov’s method[2]. Because the Maxwell’s equations are partial differential equations, it is quite natural that the initial approaches were based on calculus. However, to the authors’ impression, applications of algebraic techniques are very limited for antenna theories while a number of available mathematical tools do exist. In this talk, some trials are described. It is shown that there are rich algebraic structures in the antenna arrays. Although mathematical techniques used here are well established and even ‘classic’ for mathematicians, it is hoped that antenna engineers may find something ‘modern’ flavor.