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A necessary condition of local solvability for pseudo-differential equations with double characteristics

Fernando Cardoso, François Trèves (1974)

Annales de l'institut Fourier

Pseudodifferential operators P ( x , D ) j = 0 + P m - j ( x , D ) are studied, from the viewpoint of local solvability and under the assumption that, micro-locally, the principal symbol factorizes as P m = Q L 2 with Q elliptic, homogeneous of degree m - 2 , and L homogeneous of degree one, satisfying the following condition : there is a point ( x 0 , ξ 0 ) in the characteristic variety L = 0 and a complex number z such that d ξ Re ( z L ) 0 at ( x 0 , ξ 0 ) and such that the restriction of Im ( z L ) to the bicharacteristic strip of Re ( z L ) vanishes of order k < + at ( x 0 , ξ 0 ) , changing sign there from minus to...

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