2009/03/24 by Luke G. Rogers, Robert S. Strichartz, Rogers, Luke G. +1
Mathematics · #28A80 #46F05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals #advanced mathematical theories #math.CA #math.FA #msc:28A80 #msc:46F05
paper · pdf · doi:10.48550/arxiv.0903.4127
38 pages
arxiv created 2009/03/24 · openalex publication_date 2009/03/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct a theory of distributions in the setting of analysis on post-critically finite self-similar fractals, and on fractafolds and products based on such fractals. The results include basic properties of test functions and distributions, a structure theorem showing that distributions are locally-finite sums of powers of the Laplacian applied to continuous functions, and an analysis of the distributions with point support. Possible future applications to the study of hypoelliptic partial differential operators are suggested.