On Products of Delta Distributions and Resultants

TL;DR

This paper establishes a mathematical identity linking the integral of delta distributions of polynomials to the delta of their resultant, revealing a deep connection in integral geometry.

Contribution

It introduces a novel identity in integral geometry connecting delta distributions of polynomials with their resultants, expanding theoretical understanding.

Findings

Proves that the integral of delta distributions of two polynomials is proportional to the delta of their resultant.

Establishes a new link between integral geometry and algebraic properties of polynomials.

Provides a mathematical foundation for future applications involving polynomial resultants.

Abstract

We prove an identity in integral geometry, showing that if $P_x$ and $Q_x$ are two polynomials, $\int {\rm d}x\, \delta(P_x) \otimes \delta(Q_x)$ is proportional to $\delta(R)$ where $R$ is the resultant of $P_x$ and $Q_x$.