Braun, Rüdiger W.; Meise, Reinhold; Taylor, B. A. Surjectivity of constant coefficient partial differential operators on \({\mathcal A}(\mathbb{R}^4)\) and Whitney’s \(C_4\)-cone. (English) Zbl 1004.35032 Bull. Soc. R. Sci. Liège 70, No. 4-6, 195-206 (2001). Summary: Constant coefficient partial differential operators on the space of all real analytic functions in four variables are considered. The variety of their symbol is decomposed using methods of algorithmic algebraic geometry. This decomposition is needed for the application of a geometric characterization, given recently by the present authors, of those operators whose symbol satisfies Hörmander’s Phragmén-Lindelöf condition, which, by earlier work of Hörmander, is equivalent to the surjectivity of the differential operator on the space of real analytic functions. Cited in 4 Documents MSC: 35E10 Convexity properties of solutions to PDEs with constant coefficients 14Q10 Computational aspects of algebraic surfaces Keywords:Gröbner bases; decomposition; Hörmander’s Phragmén-Lindelöf condition PDFBibTeX XMLCite \textit{R. W. Braun} et al., Bull. Soc. R. Sci. Liège 70, No. 4--6, 195--206 (2001; Zbl 1004.35032)