Geodesic
Amibes de sommes d’exponentielles
Canadian journal of mathematics, Tome 60 (2008) no. 1, pp. 222-240

Voir la notice de l'article provenant de la source Cambridge University Press

L’objectif de cet article est d’étudier la notion d’amibe au sens de Favorov pour les systèmes finis de sommes d’exponentielles à fréquences réelles et de montrer que, sous des hypothèses de généricité sur les fréquences, le complémentaire de l’amibe d’un système de $(k\,+\,1)$ sommes d’exponentielles à fréquences réelles est un sous-ensemble $k$ -convexe au sens d’Henriques.
DOI : 10.4153/CJM-2008-010-5
Mots-clés : Primaire, 32A60, secondaire, 42A75, 55 
Silipo, James. Amibes de sommes d’exponentielles. Canadian journal of mathematics, Tome 60 (2008) no. 1, pp. 222-240. doi: 10.4153/CJM-2008-010-5
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[1] [1] Einsideler, M., Kapranov, M. et Lind, D., Non-Archimedian amoebas and tropical varieties. Preprint arXiv:math. AG/0408311 v1, 2004. Google Scholar

[2] [2] Eisenbud, D., Commutative Algebra with a View Towards Algebraic Geometry. Graduate Texts in Math. 150, Springer–Verlag, New York, 1995. Google Scholar

[3] [3] Favorov, S., Holomorphic almost periodic functions in tube domains and their amoebas. Comput. Methods Funct. Theory 1(2001), 403–415. Google Scholar

[4] [4] Forsberg, M., Amoebas and Laurent Series. Doctoral thesis, Royal Institut of Technology, Stockholm, 1998. Google Scholar

[5] [5] Forsberg, M., Passare, M. et Tsikh, A., Laurent determinants and arrangements of hyperplane amoebas. Adv. in Math. 151(2000), 45–70. Google Scholar

[6] [6] Gelfand, I. M., Kapranov, M. M. et Zelevinsky, A. V., Discriminants, Resultants and multidimensional Determinants. Birkhaüser, Boston, 1994. Google Scholar

[7] [7] Henriques, A., An analogue of convexity for complements of amoebas of varieties of higher codimension, an answer to a question asked by B. Sturmfels. Adv. in Geom. 4(2004), 61–73. Google Scholar

[8] [8] Kazarnovski, B. Ja., On the zeros of exponential sums. Soviet Math. Dokl. 23(1981), 347–351. Google Scholar

[9] [9] Meyer, Y., Algebraic Numbers and Harmonic Analysis. North-Holland, 1972. Google Scholar

[10] [10] Mikhalkin, G., Real algebraic curves, moment map and amoebas. Ann. of Math. 151(2000), 309–326. Google Scholar

[11] [11] Mikhalkin, G., Amoebas of Algebraic Varieties and Tropical Geometry. Preprint, arXiv:math. AG/0403015 v1, 2004. Google Scholar

[12] [12] Passare, M. et Rullg°ard, H., Amoebas, Monge–Ampère measures and triangulations of the Newton Polytope. Duke Math. J. 121(2004), 481–507. Google Scholar

[13] [13] Ronkin, L., On the zeros of almost periodic function generated by holomorphic functions in a multicircular domain. Complex analysis in ModernMathematics, Fazis, Moscow, (2000), 243–256 (Russian). Google Scholar

[14] [14] Rullg°ard, H., Polynomial Amoebas and Convexity. Preprint, Stokholm University, 2000. Google Scholar

[15] [15] Rullg°ard, H., Stratification des espaces de polynômes de Laurent et structure de leurs amibes. C. R. Acad. Sci. Paris Sér. I Math. 331(2000), 355–358. Google Scholar

[16] [16] Yger, A., Fonctions définies dans le plan et moyennes en tout point de leurs valeurs aux sommets de deux carrés. C. R. Acad. Sci. Paris Sér. A 288(1979), A535–A538. Google Scholar

[17] [17] Rullg°ard, H., Une généralisation d’un théorème de J. Delsarte. C. R. Acad. Sci. Paris Sér. A 288(1979), A497–A499. Google Scholar

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