Germination phenomena

TL;DR

This paper introduces a germination theorem for analytic propagation in complete normed fields and develops analogs of classical theorems, providing new insights into the geometry of zero sets of hyperbolic polynomials.

Contribution

It presents a new germination theorem for analytic propagation and generalizes classical theorems to broader contexts, enhancing understanding of hyperbolic polynomial zero sets.

Findings

Established a germination theorem for complete normed fields

Developed analogs of classical theorems in complex analysis

Gained insights into the geometry of hyperbolic polynomial zero sets

Abstract

Many theorems in complex analysis propagate analyticity, such as the Forelli theorem, edge-of-the-wedge theorem and so on. We give a germination theorem which allows for general analytic propagation in complete normed fields. In turn, we develop general analogs of the Forelli theorem, edge-of-the-wedge theorem, and the royal road theorem, and gain insight into the geometry of the zero sets of hyperbolic polynomials.