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arXiv · 1711.04140

Surjectivity of Euler operators on temperate distributions

Dietmar Vogt
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Abstract

Euler operators are partial differential operators of the form $P(\theta)$ where $P$ is a polynomial and $\theta_j = x_j \partial/\partial x_j$. We show that every non-trivial Euler operator is surjective on the space of temperate distributions on $R^d$. This is in sharp contrast to the behaviour of such operators when acting on spaces of differentiable or analytic functions.

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Dietmar Vogt. 2017-11-11. Surjectivity of Euler operators on temperate distributions. https://doi.org/10.1016/j.jmaa.2018.06.063

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