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Symmetry, Integrability and Geometry: Methods and Applications, 2020, Volume 16, 083, 11 pp.
DOI: https://doi.org/10.3842/SIGMA.2020.083 (Mi sigma1620) 		 
On Products of Delta Distributions and Resultants

Michel Bauerabcde, Jean-Bernard Zuberfg

a Département de mathematiques et applications, École normale supérieure, F-75005 Paris, France
b CNRS, UMR 8553, DMA, ENS, F-75005 Paris, France
c CNRS, UMR 3681, IPhT, F-91191 Gif-sur-Yvette, France
d PSL Research University, F-75005 Paris, France
e Institut de Physique Théorique de Saclay, CEA-Saclay, F-91191 Gif-sur-Yvette, France
f Sorbonne Université, UMR 7589, LPTHE, F-75005, Paris, France
g CNRS, UMR 7589, LPTHE, F-75005, Paris, France
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DOI: https://doi.org/10.3842/SIGMA.2020.083
Abstract: We prove an identity in integral geometry, showing that if $P_x$ and $Q_x$ are two polynomials, $\int \mathrm{d}x\, \delta(P_x) \otimes \delta(Q_x)$ is proportional to $\delta(R)$ where $R$ is the resultant of $P_x$ and $Q_x$.
Keywords: measures and distributions, integral geometry.
Received: June 16, 2020; in final form August 20, 2020; Published online August 25, 2020
Bibliographic databases:
Document Type: Article
MSC: 46F10, 49Q15
Language: English
Citation: Michel Bauer, Jean-Bernard Zuber, “On Products of Delta Distributions and Resultants”, SIGMA, 16 (2020), 083, 11 pp.
Citation in format AMSBIB
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