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1998 | 44 | 1 | 277-292
Tytuł artykułu

On the rings of formal solutions of polynomial differential equations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The paper establishes the basic algebraic theory for the Gevrey rings. We prove the Hensel lemma, the Artin approximation theorem and the Weierstrass-Hironaka division theorem for them. We introduce a family of norms and we look at them as a family of analytic functions defined on some semialgebraic sets. This allows us to study the analytic and algebraic properties of this rings.
Słowa kluczowe
Rocznik
Tom
44
Numer
1
Strony
277-292
Opis fizyczny
Daty
wydano
1998
Twórcy
  • Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, Ciudad Universitaria de Canto Blanco, 28 049 Madrid, Spain
Bibliografia
  • [ADM] G. R. Allan, H. G. Dale, J. P. McClure Pseudo-Banach algebras Studia Math. 40 (1971), 55-69
  • [AHV] J. M. Aroca, H. Hironaka, J. L. Vicente The Theory of the Maximal Contact Memorias de Matemática del Instituto 'Jorge Juan' 29, Madrid, 1975
  • [BR] R. Benedetti, J. J. Risler Real Algebraic and Semi-algebraic Sets Actualités Math., Hermann, Paris, 1990
  • [B] J. W. Brewer Power Series over Commutative Rings Lecture Notes in Pure and Appl. Math. 64, Marcel Dekker, New York, 1981
  • [Ca] J. Cano On the series defined by differential equations with an extension of the Puiseux polygon construction to this series Analysis 13 (1993), 103-119
  • [CC1] J. Chaumat, A. M. Chollet Sur le théorème de division de Weierstrass Studia Math. 116 (1995), 59-84
  • [CC2] J. Chaumat, A. M. Chollet Théorème de preparation dans les classes ultradifferentiables C. R. Acad. Sci. Paris Sér. I Math. 320 (1995), 1305-1310
  • [Co] P. M. Cohn Puiseux's theorem revisited J. Pure Appl. Algebra 31 (1984), 1-4
  • [G] M. Gevrey Sur la nature analytique des solutions des équations aux dérivées partielles Ann. Sci. École Norm. Sup. (3) 25 (1918), 129-190
  • [H] H. Hironaka Idealistic exponents of singularity in: Algebraic Geometry, John Hopkins Univ. Press, Baltimore, 1977, 52-125
  • [Mi] E. Maillet Sur les séries divergentes et les équations differentielles Ann. Sci. École Norm. Sup. 3 (1903), 487-518
  • [Ml] B. Malgrange Sur le théorème de Maillet Asymptot. Anal. 2 (1989), 1-4
  • [M] H. Matsumura Commutative Algebra Math. Lecture Note Ser. 56, Benjamin/Cumming Publishing Co., Reading, 1980
  • [N] M. Nagata Local Rings Robert E. Krieger Publishing Co., Huntington, 1975
  • [O] S. Ouchi Formal solutions with Gevrey type estimates of nonlinear partial differential equations J. Math. Sci. Univ. Tokyo 1 (1994), 205-237
  • [R] C. Rotthaus On the approximation theory of excellent rings Invent. Math. 88 (1987), 39-63
  • [T] J. Cl. Tougeron Sur les ensembles semi-analytiques avec conditions Gevrey au bord Ann. Sci. École Norm. Sup. (4) 27 (1994), 173-208
  • [Z1] M. A. Zurro Le théorème de division pour les séries Gevrey à plusieurs variables Preprint, University of Valladolid, Spain, 1992
  • [Z2] M. A. Zurro The Abhyankar Jung theorem revisited J. Pure Appl. Algebra 90 (1993), 257-282
  • [Z3] M. A. Zurro Series y funciones Gevrey en varias variables Ph.D. Thesis, University of Valladolid, Spain, 1994
  • [Z4] M. A. Zurro Summability 'au plus petit terme' Studia Math. 113 (1995), 197-198
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv44i1p277bwm
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