The use of D-modules to study exponential polynomials
Berenstein, C. ; Yger, A.
Banach Center Publications, Tome 31 (1995), p. 77-90 / Harvested from The Polish Digital Mathematics Library
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This is a summary of recent work where we introduced a class of D-modules adapted to study ideals generated by exponential polynomials.

Publié le : 1995-01-01
EUDML-ID : urn:eudml:doc:262768 
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     author = {Berenstein, C. and Yger, A.},
     title = {The use of D-modules to study exponential polynomials},
     journal = {Banach Center Publications},
     volume = {31},
     year = {1995},
     pages = {77-90},
     zbl = {0827.32013},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv31z1p77bwm}
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Berenstein, C.; Yger, A. The use of D-modules to study exponential polynomials. Banach Center Publications, Tome 31 (1995) pp. 77-90. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv31z1p77bwm/

[000] [1] M. F. Atiyah, Resolution of singularities and division of distributions, Comm. Pure Appl. Math. 23 (1970), 145-150. | Zbl 0188.19405

[001] [2] C. A. Berenstein, R. Gay and A. Yger, Analytic continuation of currents and division problems, Forum Math. 1 (1989), 15-51. | Zbl 0651.32005

[002] [3] C. A. Berenstein, R. Gay, A. Vidras and A. Yger, Residues and Bézout Identities, Progr. Math. 113, Birkhäuser, 1993. | Zbl 0802.32001

[003] [4] C. A. Berenstein and B. A. Taylor, Interpolation problems in ℂn with applications to harmonic analysis, J. Analyse Math. 37 (1980), 188-254. | Zbl 0464.42003

[004] [5] C.A. Berenstein and B.A. Taylor, On the geometry of interpolating varieties, in: Séminaire Lelong-Skoda 1980-81, Springer, Heidelberg, 1-25.

[005] [6] C. A. Berenstein, B. A. Taylor et A. Yger, Sur les systèmes d'équations différence-différentielles, Ann. Inst. Fourier (Grenoble) 33 (1983), 109-130.

[006] [7] C. A. Berenstein and A. Yger, Ideals generated by exponential polynomials, Adv. in Math. 60 (1986), 1-80.

[007] [8] C. A. Berenstein and A. Yger, On Łojasiewicz type inequalities for exponential polynomials, J. Math. Anal. Appl. 129 (1988), 166-195.

[008] [9] C. A. Berenstein and A. Yger, Analytic Bézout identities, Adv. in Appl. Math. 10 (1989), 51-74.

[009] [10] C. A. Berenstein and A. Yger, Effective Bézout estimates in ℚ[z1,...,zn], Acta Math. 66 (1991), 69-120.

[010] [11] C. A. Berenstein and A. Yger, Une formule de Jacobi et ses conséquences, Ann. Sci. École Norm. Sup. 24 (1991), 363-377. | Zbl 0742.32004

[011] [12] C. A. Berenstein and A. Yger, About Ehrenpreis' Fundamental Principle, in: Geometric and Algebraic Aspects in Several Complex Variables, C. A. Berenstein and D. C. Struppa (eds.), Editel, Rende, 1991, 47-61.

[012] [13] C. A. Berenstein and A. Yger, Formules de représentation intégrale et problèmes de division, in: Diophantine Approximations and Transcendental Numbers, P. Philippon (ed.), Walter de Gruyter, Berlin, 1992, 15-37. | Zbl 0765.32002

[013] [14] C. A. Berenstein and A. Yger, D-modules and exponential polynomials, Compositio Math. (1995), to appear.

[014] [15] B. Berndtsson and M. Andersson, Henkin-Ramirez formulas with weight factors, Ann. Inst. Fourier (Grenoble) 32 (1982), 91-110. | Zbl 0466.32001

[015] [16] I. N. Bernstein, The analytic continuation of generalized functions with respect to a parameter, Functional Anal. Appl. 6 (1972), 273-285. | Zbl 0282.46038

[016] [17] J.-E. Björk, Rings of Differential Operators, North-Holland, Amsterdam, 1979.

[017] [18] A. Borel, Operations on algebraic D-modules, in: Algebraic D-modules, A. Borel (ed.), Academic Press, Boston, 1987, 207-269.

[018] [19] L. Ehrenpreis, Fourier Analysis in Several Complex Variables, Wiley, 1970. | Zbl 0195.10401

[019] [20] D. I. Gurevich, Counterexamples to a problem of L. Schwartz, Functional Anal. Appl. 9 (1975), 116-120. | Zbl 0326.46020

[020] [21] L. Hörmander, The Analysis of Linear Partial Differential Operators, II, Springer, Berlin, 1983. | Zbl 0521.35002

[021] [22] M. Lejeune et B. Teissier, Quelques calculs utiles pour la résolution des singularités, Séminaire École Polytechnique, 1972, 130.

[022] [23] B. Lichtin, Generalized Dirichlet series and B-functions, Compositio Math. 65 (1988), 81-120.

[023] [24] L. Schwartz, Théorie générale des fonctions moyenne-périodiques, Ann. of Math. 48 (1947), 857-929. | Zbl 0030.15004

[024] [25] C. Sabbah, Proximité évanescente II. Equations fonctionnelles pour plusieurs fonctions analytiques, Compositio Math. 64 (1987), 213-241. | Zbl 0632.32006