A new valuation on polyhedral cones
Algebra i analiz, Tome 32 (2020) no. 1, pp. 1-11.

Voir la notice de l'article provenant de la source Math-Net.Ru

On polyhedral cones, a new family of valuations is introduced; they are valued in the space of bounded polyhedra.
Keywords: polyhedral cones, Brianchon–Gram–Sommerville relation, bounded polyhedron.
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H. Zheng; M. Zydor. A new valuation on polyhedral cones. Algebra i analiz, Tome 32 (2020) no. 1, pp. 1-11. http://geodesic.mathdoc.fr/item/AA_2020_32_1_a0/

[1] Arthur J., “The trace formula in invariant form”, Ann. of Math. (2), 114:1 (1981), 1–74 | DOI | MR | Zbl

[2] Barvinok A., Integer points in polyhedra, Zurich Lectures Adv. Math., Eur. Math. Soc. (EMS), 2008 | MR | Zbl

[3] Groemer H., “On the extension of additive functionals on classes of convex sets”, Pacific J. Math., 75:2 (1978), 397–410 | DOI | MR | Zbl

[4] Hug D., Kabluchko Z., “An inclusion-exclusion identity for normal cones of polyhedral sets”, Mathematika, 64:1 (2018), 124–136 | DOI | MR | Zbl

[5] Labesse J.-P., Waldspurger J.-L., La formule des traces tordue d{'}après le {F}riday {M}orning {S}eminar, CRM Monogr. Ser., 31, Amer. Math. Soc., Providence, RI, 2013 | DOI | MR

[6] Schneider R., “Combinatorial identities for polyhedral cones”, Algebra i analiz, 29:1 (2017), 279–295 | MR

[7] Shephard G. C., “An elementary proof of Gram's theorem for convex polytopes”, Canad. J. Math., 19 (1967), 1214–1217 | DOI | MR | Zbl

[8] Zydor M., Periods of automorphic forms over reductive subgroups, 2019, arXiv: 1903.01697 | Zbl