Fourier transformation of Sato's hyperfunctions
| dc.creator | Smirnov, A. G. | |
| dc.date | 2004-01-14 | |
| dc.date | 2004-09-30 | |
| dc.date.accessioned | 2026-07-07T05:04:32Z | |
| dc.date.available | 2026-07-07T05:04:32Z | |
| dc.description | A new generalized function space in which all Gelfand-Shilov classes $S^{\prime 0}_α$ ($α>1$) of analytic functionals are embedded is introduced. This space of {\it ultrafunctionals} does not possess a natural nontrivial topology and cannot be obtained via duality from any test function space. A canonical isomorphism between the spaces of hyperfunctions and ultrafunctionals on $R^k$ is constructed that extends the Fourier transformation of Roumieu-type ultradistributions and is naturally interpreted as the Fourier transformation of hyperfunctions. The notion of carrier cone that replaces the notion of support of a generalized function for ultrafunctionals is proposed. A Paley-Wiener-Schwartz-type theorem describing the Laplace transformation of ultrafunctionals carried by proper convex closed cones is obtained and the connection between the Laplace and Fourier transformation is established. | |
| dc.description | 34 pages, final version, accepted for publication in Adv. Math | |
| dc.identifier | https://arxiv.org/abs/math/0401151 | |
| dc.identifier | http://arxiv.org/abs/math/0401151 | |
| dc.identifier | Adv. Math. 196 (2005) 310-345 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69841 | |
| dc.subject | Functional Analysis | |
| dc.subject | Complex Variables | |
| dc.subject | 46F15; 32A45 | |
| dc.title | Fourier transformation of Sato's hyperfunctions | |
| dc.type | text |