Pseudo-differential Operators on Fractals

Details Pseudo-differential Operators on Fractals Pseudo-differential Operators on Fractals

2011-08-10

arxiv.org/abs/1108.2246v1

Mathematics

Functional Analysis

29 pages

Scientific paper

We define and study pseudo-differential operators on a class of fractals that include the post-critically finite self-similar sets and Sierpinski carpets. Using the sub-Gaussian estimates of the heat operator we prove that our operators have kernels that decay and, in the constant coefficient case, are smooth off the diagonal. Our analysis can be extended to product of fractals. While our results are applicable to a larger class of metric measure spaces with Laplacian, we use them to study elliptic, hypoelliptic, and quasi-elliptic operators on p.c.f. fractals, answering a few open questions posed in a series of recent papers. We extend our class of operators to include the so called H\"ormander hypoelliptic operators and we initiate the study of wavefront sets and microlocal analysis on p.c.f. fractals.

Affiliated with

Also associated with

No associations

Rating

Pseudo-differential Operators on Fractals does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Pseudo-differential Operators on Fractals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Pseudo-differential Operators on Fractals will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-665929