no. 3
Characterization of the linear partial differential operators with constant coefficients that admit a continuous linear right inverse
Annales de l'Institut Fourier, Tome 40 (1990) no. 3, pp. 619-655

Solving a problem of L. Schwartz, those constant coefficient partial differential operators P(D) are characterized that admit a continuous linear right inverse on ℰ(Ω) or 𝒟 ′ (Ω), Ω an open set in R n . For bounded Ω with C 1 -boundary these properties are equivalent to P(D) being very hyperbolic. For Ω=R n they are equivalent to a Phragmen-Lindelöf condition holding on the zero variety of the polynomial P.

Nous résolvons complètement un problème de L. Schwartz sur la caractérisation des opérateurs différentiels aux dérivées partielles P(D), à coefficients constants sur un ouvert Ω de R n , qui admettent un inverse à droite linéaire continu sur ℰ(Ω) ou 𝒟 ′ (Ω). Si Ω est borné à frontière de classe C 1 , ces propriétés sont équivalentes à une hyperbolicité très forte de P(D). Si Ω=R n , elles sont équivalentes à la validité d’un principe du type de Phragmén-Lindelöf sur la variété des zéros du polynôme P.

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     author = {Taylor, B. A. and Meise, R. and Vogt, Dietmar},
     title = {Characterization of the linear partial differential operators with constant coefficients that admit a continuous linear right inverse},
     journal = {Annales de l'Institut Fourier},
     pages = {619--655},
     year = {1990},
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Taylor, B. A.; Meise, R.; Vogt, Dietmar. Characterization of the linear partial differential operators with constant coefficients that admit a continuous linear right inverse. Annales de l'Institut Fourier, Tome 40 (1990) no. 3, pp. 619-655. doi: 10.5802/aif.1226

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