A study on harmonic function on Vicsek fractal

Harsha Gopalakrishnan and Srijanani Anurag Prasad

Chaos, Solitons & Fractals, 2024, vol. 181, issue C

Abstract: This paper focuses on the renormalization operator and harmonic functions on the Vicsek fractal. With the help of the Vicsek fractal, we have proven that the renormalization operator need not be unique for a fixed harmonic function. Also, a harmonic extension algorithm may or may not depend on the renormalization factor. Besides, the mean value property of harmonic functions on the Vicsek fractal, a D4-symmetric fractal, is also given.

Keywords: Vicsek fractal; Renormalization operator; Harmonic function; Mean value property (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:181:y:2024:i:c:s0960077924001589

DOI: 10.1016/j.chaos.2024.114607

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