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SIGMA 16 (2020), 083, 11 pages arXiv:2006.08301
https://doi.org/10.3842/SIGMA.2020.083
On Products of Delta Distributions and Resultants
Michel Bauer abcde and Jean-Bernard Zuber fg
a) Institut de Physique Théorique de Saclay, CEA-Saclay, F-91191 Gif-sur-Yvette, France
b) CNRS, UMR 3681, IPhT, F-91191 Gif-sur-Yvette, France
c) Département de mathématiques et applications, École normale supérieure, F-75005 Paris, France
d) CNRS, UMR 8553, DMA, ENS, F-75005 Paris, France
e) PSL Research University, F-75005 Paris, France
f) Sorbonne Université, UMR 7589, LPTHE, F-75005, Paris, France
g) CNRS, UMR 7589, LPTHE, F-75005, Paris, France
Received June 16, 2020, in final form August 20, 2020; Published online August 25, 2020
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 $Q_x$.
Key words: measures and distributions; integral geometry.
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References
- Coquereaux R., Zuber J.-B., The Horn problem for real symmetric and quaternionic self-dual matrices, SIGMA 15 (2019), 029, 34 pages, arXiv:1809.03394.
- Gelfand I.M., Shilov G.E., Generalized functions, Vol. I, Properties and operations, Academic Press, New York - London, 1964.
- Hörmander L., The analysis of linear partial differential operators, Vol. I, Distribution theory and Fourier analysis, Grundlehren der Mathematischen Wissenschaften, Vol. 256, Springer-Verlag, Berlin, 1983.
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