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

TL;DR

This paper critiques a recent theorem by showing it is already covered in prior survey literature, providing a simple proof and discussing alternative perspectives on the topic.

Contribution

It clarifies that the main theorem in the recent work is not novel, reproduces an existing proof, and discusses alternative literature viewpoints.

Findings

The main theorem is included in prior research survey.

The proof is simple and essentially due to Janssen.

The paper discusses alternative literature and critiques the recent work.

Abstract

We point out 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]. For context, we also reproduce the rather simple proof given in Ref1 (essentially due to Janssen). We also offer a brief discussion of the literature that is alternative to that given in Ref2. Specifically, we differ with Ref2 with respect to novelty, relevance, and attribution of stated results (and, to some extent, correctness of statements).