## View abstract

### Session S13 - Harmonic Analysis, Fractal Geometry, and Applications

Tuesday, July 20, 18:30 ~ 19:00 UTC-3

## Sampling and Interpolation of Cumulative Distribution Functions of Cantor Sets in $[0,1]$

### Eric Weber

#### Iowa State University, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak9223ec6a89151fb0136fa05283d3cbfd').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy9223ec6a89151fb0136fa05283d3cbfd = '&#101;sw&#101;b&#101;r' + '&#64;'; addy9223ec6a89151fb0136fa05283d3cbfd = addy9223ec6a89151fb0136fa05283d3cbfd + '&#105;&#97;st&#97;t&#101;' + '&#46;' + '&#101;d&#117;'; var addy_text9223ec6a89151fb0136fa05283d3cbfd = '&#101;sw&#101;b&#101;r' + '&#64;' + '&#105;&#97;st&#97;t&#101;' + '&#46;' + '&#101;d&#117;';document.getElementById('cloak9223ec6a89151fb0136fa05283d3cbfd').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy9223ec6a89151fb0136fa05283d3cbfd + '\'>'+addy_text9223ec6a89151fb0136fa05283d3cbfd+'<\/a>';

We consider the class of Cantor sets that are constructed from affine iterated function systems on the real line. These Cantor sets possess a cumulative distribution function (CDF), constructed from the invariant Borel probability measure associated with their iterated function systems. Under appropriate assumptions, we identify sampling schemes of such CDFs, meaning that the underlying Cantor set can be reconstructed from sufficiently many samples of its CDF. To this end, we prove that two Cantor sets have almost-nowhere intersection with respect to their corresponding invariant measures.

Joint work with Allison Byars (University of Wisconsin), Evan Camrud (Iowa State University), Steven Nathan Harding (Milwaukee School of Engineering), Sarah McCarty (Iowa State University) and Keith Sullivan (Concordia College).