Geodesic
Necessary and Sufficient Conditions for Hypoellipticity for a Class of Convolution Operators
Canadian journal of mathematics, Tome 46 (1994) no. 1, pp. 212-224

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper the Corwin's conjecture is proved, which says that if d is a function analytic near ∞, then the hypoellipticity of the convolution operator Ad , defined by for every u ∊ S'(Rn ), implies that P(x)/ logx → ∞ as x → ∞, where P(x) is the distance from x ∊ Rn to the set of complex zeros of d.
DOI : 10.4153/CJM-1994-008-1
Mots-clés : 35H25, 22E27 
Xuebo, Luo. Necessary and Sufficient Conditions for Hypoellipticity for a Class of Convolution Operators. Canadian journal of mathematics, Tome 46 (1994) no. 1, pp. 212-224. doi: 10.4153/CJM-1994-008-1
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[1] 1. Corwin, L., Necessary and Sufficient Conditions for Hypoellipticity for Certain Left Invariant Operators on Nilpotent Groups, Comm. PDE (9) 1(1984), 1–32. Google Scholar

[2] 2. Hormander, L., The Analysis of Linear Partial Differential Operators, If Springer-Verlag, Berlin, 1983. Google Scholar

[3] 3. Narasimhan, R., Several Complex Variables, The University of Chicago Press, Chicago and London, 1971. Google Scholar

[4] 4. Porter, M. H. and Weinberger, H. F., Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, New Jersey, 1967. Google Scholar

[5] 5. Barros-Neto, J., An Introduction to the Theory of Distributions, Marcel Dekker, New York, 1973. Google Scholar

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