Primordial function and ambiguity in its determination

TL;DR

This paper investigates reconstructing primordial functions from periodic functions, addressing ambiguities in the process and proposing conditions to eliminate them through modifications of Carlson's theorem.

Contribution

It introduces a modified Carlson theorem to establish conditions that prevent ambiguity in primordial function reconstruction.

Findings

Ambiguity in primordial function reconstruction can be limited to functions in space Ω'

Modification of Carlson's theorem helps eliminate reconstruction ambiguities

The study provides conditions for unambiguous primordial function determination

Abstract

We study the possibility to reconstruct the primordial function for some periodic function. The procedure includes an analytical continuation of a discrete function for Fourier coefficients computation, that introduces an ambiguity. To establish conditions under which no ambiguity appears, the modification of Carlson theorem is suggested. In a case when no subsidiary condition is imposed, ambiguity in the definition of primordial function does not go beyond the functions which belong to space $\Omega^{\prime}$.