This article is cited in 1 paper

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.

UDC: 517

MSC: Primary 47G05; Secondary 35S05

Received: 21.03.1975

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

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