On Products of Delta Distributions and Resultants

preprint2020arXivOpen access

Abstract

We prove an identity in integral geometry, showing that if PxP_x and QxQ_x are two polynomials, ∫dx δ(Px)⊗δ(Qx)\int {\rm d}x\, δ(P_x) \otimes δ(Q_x) is proportional to δ(R)δ(R) where RR is the resultant of PxP_x and QxQ_x.

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