Sierpiński Fractals and the Dimension of Their Laplacian Spectrum^†

Round 1

Reviewer 1 Report

Nice addition to theoretical considerations on the dimension of the spectrum.

Comments for author File: Comments.pdf

Author Response

Thank you very much for the careful reading and reviewing. We

are very happy that you consider our paper to be a good addition 

to the theoretical works on Laplacians on fractals.

Reviewer 2 Report

The paper analyses Laplacian spectral properties of Sierpinsky type fractals, especially infinite Sierpinski gaskets.

This propblem is of fundamental interest in wide range of contexts beyond pure fractal geometry, for instance for vibrations in heterogenuous and random media.

The paper is well illustrated and written. I could not check the correctness of all the equations, but the results appear to be sound.

It would be helpful to summarize briefly the main results of the paper in a Conclusion section. The authors should also discuss possible applications (fractal antennas for instance, see Cohen, « Fractal antennas Part 1 », Communications Quarterly, vol. 5,‎ été 1995, p. 7–22 ), and non-resolved problems in this context. Upon these minor revisions, the paper can be accepted for publication.

Author Response

Thank you very much for your valuable comments and references, all of which have been now incorporated in our revised version. We have added a new section (Section 5) summarising our work and included a sentence on practical applications in the introduction citing related references (see the penultimate paragraph on p.3) in the attached file.

Author Response File: Author Response.pdf