JournalsprimsVol. 43, No. 1pp. 39–54

Ultradifferentiable Fundamental Kernels of Linear Partial Differential Operators on Non-quasianalytic Classes of Roumieu Type

  • Angela A. Albanese

    Università del Salento, Lecce, Italy
  • José Bonet

    Universidad Politécnia de Valencia, Spain
Ultradifferentiable Fundamental Kernels of Linear Partial Differential Operators on Non-quasianalytic Classes of Roumieu Type cover
Download PDF

Abstract

Let P be a linear partial differential operator with coeffcients in the Roumieu class E{ω}(Ω). We prove that if P and its transposed operator tP are {ω}-hypoelliptic in Ω and surjective on the space E{ω}(Ω, then P has a global two-sided ultradifferentiable fundamental kernel in Ω, thus extending to the Roumieu classes the well-known analogous result of B. Malgrange in the _C_∞ class. This result is new even for Gevrey classes.

Cite this article

Angela A. Albanese, José Bonet, Ultradifferentiable Fundamental Kernels of Linear Partial Differential Operators on Non-quasianalytic Classes of Roumieu Type. Publ. Res. Inst. Math. Sci. 43 (2007), no. 1, pp. 39–54

DOI 10.2977/PRIMS/1199403806