Characterization of surjective convolution operators on Sato's hyperfunctions

Michael Langenbruch

Banach Center Publications, Tome 89 (2010), p. 185-193 / Harvested from The Polish Digital Mathematics Library

Résumé

Let $μ \in {(ℝ^{d})}^{'}$ be an analytic functional and let $T_{μ}$ be the corresponding convolution operator on Sato’s space $(ℝ^{d})$ of hyperfunctions. We show that $T_{μ}$ is surjective iff $T_{μ}$ admits an elementary solution in $(ℝ^{d})$ iff the Fourier transform μ̂ satisfies Kawai’s slowly decreasing condition (S). We also show that there are $0 \neq μ \in {(ℝ^{d})}^{'}$ such that $T_{μ}$ is not surjective on $(ℝ^{d})$ .

Publié le : 2010-01-01

Zbl 1213.46035

EUDML-ID : urn:eudml:doc:281860

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     author = {Michael Langenbruch},
     title = {Characterization of surjective convolution operators on Sato's hyperfunctions},
     journal = {Banach Center Publications},
     volume = {89},
     year = {2010},
     pages = {185-193},
     zbl = {1213.46035},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc88-0-15}
}

Michael Langenbruch. Characterization of surjective convolution operators on Sato's hyperfunctions. Banach Center Publications, Tome 89 (2010) pp. 185-193. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc88-0-15/