Abstract
For a family of Cantor measuresμ on ℝn, we construct a solution to the problem of recoveringƒ from μ *ƒ forƒ of compact support, as the limit of λ k * (μ* ƒ) where λ k is a sequence of distributions exhibiting a form of self-similarity. We also investigate Ehrenpreis’ necessary and sufficient condition on\(\hat \mu \) for there to exist a fundamental solutionλ withμ * λ =δ, and show that it depends on certain number-theoretic conditions in the description ofμ. The first result is also proved for certain self-similar measures on Heisenberg groups.
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Research supported in part by the National Science Foundation, grant DMS-9103348.
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Strichartz, R.S. A fractal Radon inversion problem. J. Anal. Math. 64, 219–240 (1994). https://doi.org/10.1007/BF03008410
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DOI: https://doi.org/10.1007/BF03008410