  This paper is a response to an article (R. de la Madrid, Journal of Physics
A: Mathematical and General, 39,9255-9268 (2006)) recently published in Journal
of Physics A: Mathematical and Theoretical. The article claims that the theory
of resonances and decaying states based on certain rigged Hilbert spaces of
Hardy functions is physically untenable. In this paper we show that all of the
key conclusions of the cited article are the result of either the errors in
mathematical reasoning or an inadequate understanding of the literature on the
subject.
