Measures Determined by the Restriction of Convolution Powers to the Proper Concave Cone

2022/02/16 by Aleksander Pawlewicz, Pawlewicz, Aleksander
Mathematics · #28A35 #Advanced Operator Algebra Research #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2202.08129

openalex publication_date 2022/02/16 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

Let μ and ν be two non-degenerate finite signed Borel measures defined on a proper convex cone of ℝⁿ. We prove that if all convolution powers of μ and ν are appropriately equal (and non-zero) on a proper concave cone of ℝⁿ, the measures are equal. A similar but more general result for measures defined on ℝ can be found in [2]. We also provide an example of two-dimensional measures, which indicates that equality of measures and their appropriate convolution powers on a half-plane is not enough for equality of measures.

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