Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Abdolmaleki, Yavar, Kucerovsky, Dan
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213262559