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A sharp density bound for infinite convolutions
Abstract
We prove a sharp L∞ bound for the density of an infinite convolution in terms of L2 norms of convolution powers of the summand densities. The bound may be finite even when every summand density is unbounded and the products arising from Young's inequality diverge.
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BibTeX
@misc{alcorta2026sharp,
title = {{A sharp density bound for infinite convolutions}},
author = {Peio Alcorta},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08643},
eprint = {2610.08643},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08643},
}
RIS
TY - UNPB
TI - A sharp density bound for infinite convolutions
AU - Peio Alcorta
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08643
UR - https://arxiv.org/abs/2610.08643
AB - We prove a sharp L^∞ bound for the density of an infinite convolution in terms of L^2 norms of convolution powers of the summand densities. The bound may be finite even when every summand density is unbounded and the products arising from Young's inequality diverge.
ER -