Weighted Bergman Kernels and Mathematical Physics

Round 1

Reviewer 1 Report

Review of manuscript axioms-687577.

Generally, the topis taking into account in the review is essential. The authors have done a lot of work into the preparation of the reviewed paper. Thus, in my opinion, the manuscript is comprehensive but requires some additions.

1. One of the hint to write an abstract is avoiding citation of the references unless the reference inspired the author to investigate further. Thus, the question is, if the references in the abstract are necessary. Please consider, rewrite the abstract.
   
2. Looking through the bibliography, one can get the impression that the number of items is large. However, after verification, it should be stated that it does not contain all available scientific studies on the subject of the review. Thus, some minor elements in the field of Weighted Bergman Kernels and Mathematical Physics may have been omitted; for example, I did not find any study by M Engliš. You can probably find the results that the authors have already discussed, but you may also find those that you missed. Please check the literature selection again and, if necessary, extend it.
   
3. The title of the paper is "Weighted Bergman Kernels and Mathematical Physics". Unfortunately, as the weighted Bergman kernels section is developed correctly and almost enough (see notes above), the section on mathematical physics is stripped down. Only fragments of this area of research can be found, which is actually a very important topic for researchers in this field. This can be demonstrated by the number of books on this subject that is available. To sum up, I would suggest supplementing, although a review of the literature, an indication of the items regarding mathematical physics and describing their content.

Finally, I suggest accepting this review after minor revision.

 

Author Response

please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Usually, the Abstract shouldn't contain cited references.

The equations should be numbered, all of them.

You should respect a common structure of the manuscript: 1-Introduction; 2-Method; etc.,..., Results, Conclusions, Acknowledgements, References.

The Reference section should be ascendent numbered for a convenient search and following process.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The manuscript isn't well structured.

Author Response

We have added two more sections, that is an Introduction and a Conclusions
section, in an attempt to comply with the "indications" of Reviewer n. 2. Also key words have been added, as a footnote to the Introduction.

 

Thanks for your efforts.