Comment on 'Comment on 'Affine density, von Neumann dimension and a problem of Perelomov"

TL;DR

This paper refutes claims made in a recent comment, clarifying that the main theorem of a referenced research paper was not included in a prior survey, and criticizes the comment's mathematical reasoning.

Contribution

It provides a detailed correction to a recent comment, clarifying misunderstandings and emphasizing the importance of accurate mathematical communication.

Findings

The main theorem is not in the prior survey.

The comment contains incorrect mathematical reasoning.

The authors call for a retraction and apology.

Abstract

In the Letter 'Comment on 'Affine density, von Neumann dimension and a problem of Perelomov', arXiv.2211.04879, by Prof. J. L. Romero, it is claimed that the main theorem of Ref2 := [Adv. Math. 407, Article ID 108564, 22 p. (2022)] is included in the prior research survey Ref1 := [Expo. Math., 40(2), 265-301, 2022]. We provide some background, and demonstrate with hard facts that this claim is false, as well as other claims in the Letter which, in most cases, either result from wrong mathematical reasoning or objectively differ from what is written in the published material. The author might be interested in publicly retracting and apologising for his comments.