Multivariate Symmetric Interpolating Dual Multiwavelet Frames

Round 1

Reviewer 1 Report

After carefully reading the paper, I think that the following issues should be addressed:

- the abstract should be extended and more information should be provided on the gap in the literature and discuss more the results

- the state of the current research should be better highlighted in the introduction

- section 2, which discuss the notations used in the paper, should contain a summative table in which the variables should be included along with their properties

- a numerical example connected to a real-life situation should be provided in order to better observe the practical application of the proposed approach

- concluding remarks should be added

- an extended discussion section is needed, in which limitations should be also presented

- a comparison with the state of the art in terms of theoretical and practical achievements should be added

Author Response

Dear Reviewer, please see the attached file.

Author Response File: Author Response.pdf

Reviewer 2 Report

See the attached report.

Comments for author File: Comments.pdf

Author Response

Dear Reviewer, please see the attached file.

Author Response File: Author Response.pdf

Reviewer 3 Report

This is an interesting most well-written article.  We have some suggestions for improvements, listed below.

1. There are some small issues with English in the writing.  We list some typical examples from Page 3below, and suggest that the authors give the entire paper a careful review to correct these types of issues.

Just before equation (1):  Instead of "a bit different", it would be better to say "a slightly different".

Slightly below that: Instead of "allows to", use "allows us to".

Line 97: Instead of "from the group theory", use "from group theory".


2. The papers by Geronimo on Hardin on multiwavelets played an important role in the early development of the field.  It would be appropriate to cite some of these papers in the introduction.


3. It would be very nice if the authors could include some figures to illustrate the examples in Section 5.

Author Response

Dear Reviewer, please see the attached file.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Thank you for the revised version of the paper and for the changes made. I have no further observations.