Geodesic
Complex powers of hypoelliptic systems in~$\mathbf R^n$
Sbornik. Mathematics, Tome 28 (1976) no. 3, pp. 291-300

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A system of differential operators in $\mathbf R^n$ with polynomial coefficients and whose symbol is hypoelliptic in $(x;\xi)$ is considered. The complex powers and the zeta-function of such a system are constructed. A meromorphic extension of the zeta-function is obtained, from which there follows an asymptotic result concerning the spectrum of the system. The results of Hironaka on the resolution of singularities are used in the proofs. Bibliography: 9 titles. 
@article{SM_1976_28_3_a1,
     author = {S. A. Smagin},
     title = {Complex powers of hypoelliptic systems in~$\mathbf R^n$},
     journal = {Sbornik. Mathematics},
     pages = {291--300},
     publisher = {mathdoc},
     volume = {28},
     number = {3},
     year = {1976},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1976_28_3_a1/}
}
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S. A. Smagin. Complex powers of hypoelliptic systems in~$\mathbf R^n$. Sbornik. Mathematics, Tome 28 (1976) no. 3, pp. 291-300. http://geodesic.mathdoc.fr/item/SM_1976_28_3_a1/