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Mat. Sb. (N.S.), 1976, Volume 99(141), Number 3, Pages 331–341 (Mi msb2753)  

Complex powers of hypoelliptic systems in $\mathbf R^n$

S. A. Smagin


Abstract: 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.

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English version:
Mathematics of the USSR-Sbornik, 1976, 28:3, 291–300

Bibliographic databases:

UDC: 517
MSC: Primary 47G05; Secondary 35S05
Received: 21.03.1975

Citation: S. A. Smagin, “Complex powers of hypoelliptic systems in $\mathbf R^n$”, Mat. Sb. (N.S.), 99(141):3 (1976), 331–341; Math. USSR-Sb., 28:3 (1976), 291–300

Citation in format AMSBIB
\Bibitem{Sma76}
\by S.~A.~Smagin
\paper Complex powers of hypoelliptic systems in~$\mathbf R^n$
\jour Mat. Sb. (N.S.)
\yr 1976
\vol 99(141)
\issue 3
\pages 331--341
\mathnet{http://mi.mathnet.ru/msb2753}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=417560}
\zmath{https://zbmath.org/?q=an:0346.35029}
\transl
\jour Math. USSR-Sb.
\yr 1976
\vol 28
\issue 3
\pages 291--300
\crossref{https://doi.org/10.1070/SM1976v028n03ABEH001652}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1976EM69200002}


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