On the applications of Hardy class functions in scattering theory

TL;DR

This paper defends the use of Hardy class functions in scattering theory, countering recent criticisms by clarifying mathematical reasoning and literature understanding.

Contribution

It refutes claims that the Hardy function approach in resonance theory is physically untenable, reaffirming its validity.

Findings

Corrects mathematical errors in previous critique

Clarifies the theoretical foundations of Hardy functions in scattering

Reaffirms the physical relevance of Hardy class functions

Abstract

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.