Characterization of the linear partial differential operators with constant coefficients that admit a continuous linear right inverse

Taylor, B. A.; Meise, R.; Vogt, Dietmar

doi:10.5802/aif.1226

Taylor, B. A. ; Meise, R. ; Vogt, Dietmar

Annales de l'Institut Fourier, Tome 40 (1990) no. 3, pp. 619-655.

Résumé
Abstract

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 $P$ .

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 $P$ .

MR Zbl | 3 citations dans Numdam

DOI : 10.5802/aif.1226

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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},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {40},
     number = {3},
     year = {1990},
     doi = {10.5802/aif.1226},
     mrnumber = {92e:46083},
     zbl = {0703.46025},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.1226/}
}

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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. http://www.numdam.org/articles/10.5802/aif.1226/

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