Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-24T13:18:26.451Z Has data issue: false hasContentIssue false
  • English
  • Français

Amibes de sommes d’exponentielles

Published online by Cambridge University Press:  20 November 2018

James Silipo
James Silipo*
Affiliation:
LaBAG, Institut de Mathématiques, U.F.R. de Mathématiques et Informatique, Université Bordeaux 1, 351 cours de la Libération, 33405, Talence Cedex, France e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Résumé

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Keywords

Primaire32A60secondaire42A7555
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 60 , Issue 1 , 01 February 2008 , pp. 222 - 240
Copyright
Copyright © Canadian Mathematical Society 2008

References

[1] Einsideler, M., Kapranov, M. et Lind, D., Non-Archimedian amoebas and tropical varieties. Preprint arXiv:math. AG/0408311 v1, 2004.Google Scholar
[2] Eisenbud, D., Commutative Algebra with a View Towards Algebraic Geometry. Graduate Texts in Math. 150, Springer–Verlag, New York, 1995.Google Scholar
[3] Favorov, S., Holomorphic almost periodic functions in tube domains and their amoebas. Comput. Methods Funct. Theory 1(2001), 403–415.Google Scholar
[4] Forsberg, M., Amoebas and Laurent Series. Doctoral thesis, Royal Institut of Technology, Stockholm, 1998.Google Scholar
[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] Gelfand, I. M., Kapranov, M. M. et Zelevinsky, A. V., Discriminants, Resultants and multidimensional Determinants. Birkhaüser, Boston, 1994.Google Scholar
[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] Kazarnovski, B. Ja., On the zeros of exponential sums. Soviet Math. Dokl. 23(1981), 347–351.Google Scholar
[9] Meyer, Y., Algebraic Numbers and Harmonic Analysis. North-Holland, 1972.Google Scholar
[10] Mikhalkin, G., Real algebraic curves, moment map and amoebas. Ann. of Math. 151(2000), 309–326.Google Scholar
[11] Mikhalkin, G., Amoebas of Algebraic Varieties and Tropical Geometry. Preprint, arXiv:math. AG/0403015 v1, 2004.Google Scholar
[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] 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] Rullg°ard, H., Polynomial Amoebas and Convexity. Preprint, Stokholm University, 2000.Google Scholar
[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] 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] Rullg°ard, H., Une généralisation d’un théorème de J. Delsarte. C. R. Acad. Sci. Paris Sér. A 288(1979), A497–A499.Google Scholar