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

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.