Differential operators of the first order with degenerate principal symbols

• Autorzy: Rainer Felix
• Języki publikacji: EN

Abstrakty

EN

Let there be given a differential operator on $ℝ^n$ of the form $D = ∑^{n}_{i,j=1} a_{ij}·x_j ∂/∂x_i + μ$, where $A = (a_{ij})$ is a real matrix and μ is a complex number. We study the following question: To what extent the mapping $D :S'(ℝ^n) → S'(ℝ^n)$ is surjective? We shall give some conditions on A and μ which assure the surjectivity of D.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1992
• Tom: 27
• Numer: 1
• Strony: 147-161

Daty

wydano

1992

Twórcy

autor

Rainer Felix

• Mathematisch-Geographische Fakultät, Katholische Universität Eichstätt, Ostenstr. 28, D-8078 Eichstätt, Germany

Bibliografia

• [1] R. Felix, Solvability of differential equations with linear coefficients of nilpotent type, Proc. Amer. Math. Soc. 94 (1985), 161-166.
• [2] R. Felix, Zentrale Distributionen auf Exponentialgruppen, J. Reine Angew. Math. 389 (1988), 133-156.
• [3] G. B. Folland, Real Analysis. Modern Techniques and Their Applications, Wiley, New York 1984.
• [4] L. Hörmander, On the division of distributions by polynomials, Ark. Mat. 3 (1958), 555-568.
• [5] L. Hörmander, The Analysis of Linear Partial Differential Operators I, Springer, Berlin 1983.
• [6] D. Müller and F. Ricci, Analysis of second order differential operators on Heisenberg groups II, preprint.
• [7] H. H. Schaefer, Topological Vector Spaces, 5th printing, Springer, New York 1986.
• [8] L. Schwartz, Théorie des distributions, Hermann, Paris 1966.