Sampling and interpolation of cumulative distribution functions of Cantor sets in [0, 1]

• Autorzy: Byars Allison , Camrud Evan , Harding Steven N. , McCarty Sarah , Sullivan Keith , Weber Eric S.

Identyfikatory

DOI

10.1515/dema-2021-0010

• Języki publikacji: EN

Abstrakty

EN

Cantor sets are constructed from iteratively removing sections of intervals. This process yields 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.

Słowa kluczowe

EN

fractal; Cantor set; sampling; interpolation; normal numbers

PL

fraktal; zbiór Cantora; próbkowanie; interpolacja

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2021
• Tom: Vol. 54, nr 1
• Strony: 85--109
• Opis fizyczny: Bibliogr. 26 poz., rys.

Twórcy

autor

Byars Allison

• Department of Mathematics, University of Wisconsin Madison, 480 Lincoln Drive, Madison, WI 53706, USA

autor

Camrud Evan

• Department of Mathematics, Iowa State University, 411 Morrill Road, Ames, IA 50011, USA

autor

Harding Steven N.

• Department of Mathematics, Milwaukee School of Engineering, 500 E. Kilbourn Ave., Milwaukee, WI 53202, USA

autor

McCarty Sarah

• Department of Mathematics, Iowa State University, 411 Morrill Road, Ames, IA 50011, USA

autor

Sullivan Keith

• Department of Mathematics, Concordia College, 901 8th St. S. Moorhead, MN 56562, USA

autor

Weber Eric S.

• Department of Mathematics, Iowa State University, 411 Morrill Road, Ames, IA 50011, USA

Bibliografia

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Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).