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1995 | 31 | 1 | 77-90
Tytuł artykułu

The use of D-modules to study exponential polynomials

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This is a summary of recent work where we introduced a class of D-modules adapted to study ideals generated by exponential polynomials.
Słowa kluczowe
Rocznik
Tom
31
Numer
1
Strony
77-90
Opis fizyczny
Daty
wydano
1995
Twórcy
  • Mathematics Department & Institute of Systems Research, University of Maryland, College Park, Maryland 20742, U.S.A.
autor
  • Département de Mathématiques, Université de Bordeaux I, 33405 Talence, France
Bibliografia
  • [1] M. F. Atiyah, Resolution of singularities and division of distributions, Comm. Pure Appl. Math. 23 (1970), 145-150.
  • [2] C. A. Berenstein, R. Gay and A. Yger, Analytic continuation of currents and division problems, Forum Math. 1 (1989), 15-51.
  • [3] C. A. Berenstein, R. Gay, A. Vidras and A. Yger, Residues and Bézout Identities, Progr. Math. 113, Birkhäuser, 1993.
  • [4] C. A. Berenstein and B. A. Taylor, Interpolation problems in $ℂ^n$ with applications to harmonic analysis, J. Analyse Math. 37 (1980), 188-254.
  • [5] C.A. Berenstein and B.A. Taylor, On the geometry of interpolating varieties, in: Séminaire Lelong-Skoda 1980-81, Springer, Heidelberg, 1-25.
  • [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.
  • [7] C. A. Berenstein and A. Yger, Ideals generated by exponential polynomials, Adv. in Math. 60 (1986), 1-80.
  • [8] C. A. Berenstein and A. Yger, On Łojasiewicz type inequalities for exponential polynomials, J. Math. Anal. Appl. 129 (1988), 166-195.
  • [9] C. A. Berenstein and A. Yger, Analytic Bézout identities, Adv. in Appl. Math. 10 (1989), 51-74.
  • [10] C. A. Berenstein and A. Yger, Effective Bézout estimates in $ℚ[z_1,...,z_n]$, Acta Math. 66 (1991), 69-120.
  • [11] C. A. Berenstein and A. Yger, Une formule de Jacobi et ses conséquences, Ann. Sci. École Norm. Sup. 24 (1991), 363-377.
  • [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.
  • [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.
  • [14] C. A. Berenstein and A. Yger, D-modules and exponential polynomials, Compositio Math. (1995), to appear.
  • [15] B. Berndtsson and M. Andersson, Henkin-Ramirez formulas with weight factors, Ann. Inst. Fourier (Grenoble) 32 (1982), 91-110.
  • [16] I. N. Bernstein, The analytic continuation of generalized functions with respect to a parameter, Functional Anal. Appl. 6 (1972), 273-285.
  • [17] J.-E. Björk, Rings of Differential Operators, North-Holland, Amsterdam, 1979.
  • [18] A. Borel, Operations on algebraic D-modules, in: Algebraic D-modules, A. Borel (ed.), Academic Press, Boston, 1987, 207-269.
  • [19] L. Ehrenpreis, Fourier Analysis in Several Complex Variables, Wiley, 1970.
  • [20] D. I. Gurevich, Counterexamples to a problem of L. Schwartz, Functional Anal. Appl. 9 (1975), 116-120.
  • [21] L. Hörmander, The Analysis of Linear Partial Differential Operators, II, Springer, Berlin, 1983.
  • [22] M. Lejeune et B. Teissier, Quelques calculs utiles pour la résolution des singularités, Séminaire École Polytechnique, 1972, 130.
  • [23] B. Lichtin, Generalized Dirichlet series and B-functions, Compositio Math. 65 (1988), 81-120.
  • [24] L. Schwartz, Théorie générale des fonctions moyenne-périodiques, Ann. of Math. 48 (1947), 857-929.
  • [25] C. Sabbah, Proximité évanescente II. Equations fonctionnelles pour plusieurs fonctions analytiques, Compositio Math. 64 (1987), 213-241.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv31z1p77bwm
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