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The characterization of differential operators by locality: Classical flows. (English) Zbl 0606.47048

It is known that partial differential operators can be characterized by locality. The authors prove that a linear operator H from \(C_ 0^{\infty}(X)\) into the space \(C_ b(X)\) of bounded continuous functions satisfies the locality condition \[ \sup p(Hf)\subseteq \sup p(f),\quad f\in C_ 0^{\infty}(X) \] iff it is a polynomial in \(\delta_ i\), where \((\delta_ 1,\delta_ 2,...,\delta_{\nu})\) are infinitesimal generators of a certain action \(\tau\). Consequences and related results are shown.
Reviewer: C.Badea-Simionescu

MSC:

47F05 General theory of partial differential operators
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References:

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