Hadamard type operators on temperate distributions
| Autor: | Vogt, Dietmar |
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| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We study Hadamard operators on $S'(R^d)$ and give a complete characterization. They have the form $L(S)=S*T$ where * here means the multiplicative convolution and T is in the space of distributions which are $\theta$-rapidly decreasing in infinity and at the coordinate hyperplanes. To show this we study and characterize convolution operators on the space $Y(R^d)$ of exponentially decreasing $C^\infty$-functions on $R^d$. We use this and the exponential transformation to characterize the Hadamard operators on $S'(Q)$, $Q$ the positive quadrant, and this result we use as a building block for our main result. |
| Databáze: | arXiv |
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