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Shannon Integrals and Applications to Reimann-Hilbert Problems
Abstract
We say that a function f can be represented by a Shannon integral if it can be written as the integral of sin(xs)/(xs), with respect to some finite measure. We develop a theory of Shannon integral representations for positive definite functions and show that under mild conditions f can be written as sum of two positive definite functions that constitute solutions to an additive Reimann_Hilbert problem on real line.
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BibTeX
@misc{abdolmaleki2026shannon,
title = {{Shannon Integrals and Applications to Reimann-Hilbert Problems}},
author = {Yavar Abdolmaleki and Dan Kucerovsky},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15805},
eprint = {2609.15805},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15805},
}
RIS
TY - UNPB
TI - Shannon Integrals and Applications to Reimann-Hilbert Problems
AU - Yavar Abdolmaleki
AU - Dan Kucerovsky
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15805
UR - https://arxiv.org/abs/2609.15805
AB - We say that a function f can be represented by a Shannon integral if it can be written as the integral of sin(xs)/(xs), with respect to some finite measure. We develop a theory of Shannon integral representations for positive definite functions and show that under mild conditions f can be written as sum of two positive definite functions that constitute solutions to an additive Reimann_Hilbert problem on real line.
ER -