Physical bounds and summation rules in antenna theory

Although the concept of physical bounds for electrically small antennas was first introduced more than half a century
ago by Wheeler and Chu it continuous to receive attention and still there is only a partial knowledge of these bounds.
Most of the research effort in this field are based on the ideas of a stored energy in the different partial waves as
introduced by Chu and, hence, suffers from the same shortcomings. The objective of this paper is to present three
alternative approaches to derive physical bounds on antennas that are solely based on the assumptions of linearity, timetranslational
invariance, causality, and reciprocity. These assumptions are utilized in three different scattering settings
to construct various Herglotz functions from which summation rules and associated physical bounds are derived.