The spaces OM and OC are ultrabornological a new proof
In [1] Laurent Schwartz introduced the spaces 𝒪M and 𝒪′C of multiplication and convolution operators on temperate distributions. Then in [2] Alexandre Grothendieck used tensor products to prove that both 𝒪M and 𝒪′C are bornological. Our proof of this property is more constructive and based on dualit...
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| Format: | Article |
| Language: | English |
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Wiley
1985-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171285000904 |
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| _version_ | 1832552878368096256 |
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| author | Jan Kucera |
| author_facet | Jan Kucera |
| author_sort | Jan Kucera |
| collection | DOAJ |
| description | In [1] Laurent Schwartz introduced the spaces 𝒪M and 𝒪′C of multiplication and convolution operators on temperate distributions. Then in [2] Alexandre Grothendieck used tensor products to prove that both 𝒪M and 𝒪′C are bornological. Our proof of this property is more constructive and based on duality. |
| format | Article |
| id | doaj-art-bac37492483b49f7a3b0226f64bab7a5 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1985-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-bac37492483b49f7a3b0226f64bab7a52025-02-03T05:57:38ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251985-01-018481381610.1155/S0161171285000904The spaces OM and OC are ultrabornological a new proofJan Kucera0Department of Mathematics, Washington State University, Pullman, Washington 99164-2930, USAIn [1] Laurent Schwartz introduced the spaces 𝒪M and 𝒪′C of multiplication and convolution operators on temperate distributions. Then in [2] Alexandre Grothendieck used tensor products to prove that both 𝒪M and 𝒪′C are bornological. Our proof of this property is more constructive and based on duality.http://dx.doi.org/10.1155/S0161171285000904temperate distributionmultiplication and convolutioninductive and projective limitbornologicalreflexiveand Schwartz spaces. |
| spellingShingle | Jan Kucera The spaces OM and OC are ultrabornological a new proof International Journal of Mathematics and Mathematical Sciences temperate distribution multiplication and convolution inductive and projective limit bornological reflexive and Schwartz spaces. |
| title | The spaces OM and OC are ultrabornological a new proof |
| title_full | The spaces OM and OC are ultrabornological a new proof |
| title_fullStr | The spaces OM and OC are ultrabornological a new proof |
| title_full_unstemmed | The spaces OM and OC are ultrabornological a new proof |
| title_short | The spaces OM and OC are ultrabornological a new proof |
| title_sort | spaces om and oc are ultrabornological a new proof |
| topic | temperate distribution multiplication and convolution inductive and projective limit bornological reflexive and Schwartz spaces. |
| url | http://dx.doi.org/10.1155/S0161171285000904 |
| work_keys_str_mv | AT jankucera thespacesomandocareultrabornologicalanewproof AT jankucera spacesomandocareultrabornologicalanewproof |