Geodesic
A Fundamental Solution for a Nonelliptic Partial Differential Operator
Canadian journal of mathematics, Tome 31 (1979) no. 5, pp. 1107-1120

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

Let (1) and set (2) Here . Z is the “unique” (modulo multiplication by nonzero functions) holomorphic vector-field which is tangent to the boundary of the “degenerate generalized upper half-plane” (3) In our terminology t = Re z 1. We note that L is nowhere elliptic. To put it into context, L is of the type □b , i.e. operators like L occur in the study of the boundary Cauchy-Riemann complex. For more information concerning this connection the reader should consult [1] and [2]. 
Greiner, Peter C. A Fundamental Solution for a Nonelliptic Partial Differential Operator. Canadian journal of mathematics, Tome 31 (1979) no. 5, pp. 1107-1120. doi: 10.4153/CJM-1979-101-3
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[1] 1. Greiner, P. C. and Stein, E. M., Estimates for the d-Neumann problem, Mathematical Notes Series, 19 (Princeton Univ. Press, Princeton, N.J., 1977). Google Scholar

[2] 2. Greiner, P. C. and Stein, E. M., On the solvability of some differential operators of type \b, Seminar on Several Complex Variables, Cortona, Italy, 1976. Google Scholar

[3] 3. Hôrmander, L., Hypoelliptic second order differential equations, Acta Math. 119 (1967), 147–171. Google Scholar

[4] 4. Kohn, J. J., Harmonic integrals for differential complexes, Global Analysis, Princeton Math. Series, 29 (Princeton Univ. Press, Princeton, N.J., 1969), 295–308. Google Scholar

[5] 5. Rothschild, L. P. and Stein, E. M., Hypoelliptic differential operators and nilpotent groups, Acta Math. 137 (1976), 247–320. Google Scholar

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