Geodesic
Pseudodifferential Resolvent for a Certain Non-Locally-Solvable Operator
Canadian journal of mathematics, Tome 26 (1974) no. 5, pp. 1130-1140

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

In this note we construct a pseudo-differential resolvent for by the method of [3] and study the dependence on the parameter λ as λ → 1. Grushin [2] first pointed out that P is solvable and hypoelliptic if λ is not an odd integer, whereas P is neither locally solvable at the origin nor hypoelliptic if λ is an odd integer. Gilioli and Trèves [1] showed that this discrete nature of the condition for solvability persists to a more general class of operators. 
Hoel, C. Pseudodifferential Resolvent for a Certain Non-Locally-Solvable Operator. Canadian journal of mathematics, Tome 26 (1974) no. 5, pp. 1130-1140. doi: 10.4153/CJM-1974-105-9
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[1] 1. Gilioli, A. and Treves, F., An example in the solvability theory of linear PDE's, Amer. J. Math. (to appear). Google Scholar

[2] 2. Grushin, V., Les problèmes aux limites dégénères et les operateurs pseudo-differentiels, Actes, Congres Intern. Math., 1970, Tome 2, p. 737 a 743. Google Scholar

[3] 3. Hoel, C., Fundamental solutions of some degenerate operators (to appear). Google Scholar

[4] 4. Riesz, F. and Sz.-Nagy, B., Functional analysis (F. Ungar Pub. Co., New York, 1955). Google Scholar

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