Geodesic
Local solvability of pseudodifferential operators with characteristics of second multiplicity
Sbornik. Mathematics, Tome 29 (1976) no. 2, pp. 193-216

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A study is made of the local properties of operators whose leading symbol admits a representation in the form of a sum (difference) of squares of operators of principal type. The coefficients are infinitely smooth and are not necessarily of power growth. Necessary and sufficient conditions are formulated in the invariant language of null bicharacteristics and of the subprincipal symbol. Definitive results are obtained for some special classes of equations. The work extends results obtained earlier by the author for operators whose leading symbol is the square of an operator of principal type. Bibliography: 27 titles. 
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     author = {P. R. Popivanov},
     title = {Local solvability of pseudodifferential operators with characteristics of second multiplicity},
     journal = {Sbornik. Mathematics},
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     volume = {29},
     number = {2},
     year = {1976},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1976_29_2_a5/}
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P. R. Popivanov. Local solvability of pseudodifferential operators with characteristics of second multiplicity. Sbornik. Mathematics, Tome 29 (1976) no. 2, pp. 193-216. http://geodesic.mathdoc.fr/item/SM_1976_29_2_a5/