Prescribing analytic singularities for solutions of a class of vector fields on the torus |
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| Authors: | Adalberto P. Bergamasco Sé rgio Luí s Zani |
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| Affiliation: | Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação - USP, Caixa Postal 668, São Carlos, SP, 13560-970 Brasil ; Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação - USP, Caixa Postal 668, São Carlos, SP, 13560-970 Brasil |
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| Abstract: | We consider the operator  acting on distributions on the two-torus  where  and  are real-valued, real analytic functions defined on the unit circle  We prove, among other things, that when  changes sign, given any subset  of the set of the local extrema of the local primitives of  there exists a singular solution of  such that the  projection of its analytic singular support is  furthermore, for any  and any closed subset  of  there exists  such that  and  We also provide a microlocal result concerning the trace of  at  |
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| Keywords: | Analytic singularities global analytic hypoellipticity stationary phase |
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