Vector-valued Fourier hyperfunctions and boundary values
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arXiv
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866910136590663680 |
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| author | Kruse, Karsten |
| author_facet | Kruse, Karsten |
| contents | This work is dedicated to the development of the theory of Fourier hyperfunctions in one variable with values in a complex non-necessarily metrisable locally convex Hausdorff space $E$. Moreover, necessary and sufficient conditions are described such that a reasonable theory of $E$-valued Fourier hyperfunctions exists. In particular, if $E$ is an ultrabornological PLS-space, such a theory is possible if and only if E satisfies the so-called property $(PA)$. Furthermore, many examples of such spaces having $(PA)$ resp. not having $(PA)$ are provided. We also prove that the vector-valued Fourier hyperfunctions can be realized as the sheaf generated by equivalence classes of certain compactly supported $E$-valued functionals and interpreted as boundary values of slowly increasing holomorphic functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1912_03659 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Vector-valued Fourier hyperfunctions and boundary values Kruse, Karsten Functional Analysis Complex Variables 32A45, 46F15, 35A01, 46A13, 46A63, 46M20 This work is dedicated to the development of the theory of Fourier hyperfunctions in one variable with values in a complex non-necessarily metrisable locally convex Hausdorff space $E$. Moreover, necessary and sufficient conditions are described such that a reasonable theory of $E$-valued Fourier hyperfunctions exists. In particular, if $E$ is an ultrabornological PLS-space, such a theory is possible if and only if E satisfies the so-called property $(PA)$. Furthermore, many examples of such spaces having $(PA)$ resp. not having $(PA)$ are provided. We also prove that the vector-valued Fourier hyperfunctions can be realized as the sheaf generated by equivalence classes of certain compactly supported $E$-valued functionals and interpreted as boundary values of slowly increasing holomorphic functions. |
| title | Vector-valued Fourier hyperfunctions and boundary values |
| topic | Functional Analysis Complex Variables 32A45, 46F15, 35A01, 46A13, 46A63, 46M20 |
| url | https://arxiv.org/abs/1912.03659 |