Fischer decompositions for entire functions of sufficiently low order
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908745019162624 |
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| author | Aldaz, J. M. Render, H. |
| author_facet | Aldaz, J. M. Render, H. |
| contents | The existence of decompositions of the form $f=P\cdot q+r$ with $P_k^{\ast}\left( D\right) r=0$, where $f$ is entire, $P$ a polynomial and $P^{\ast}_k$ the principal part of $P$ with its coefficients conjugated, was achieved in \cite{AlRe23} under certain restrictions on the order of $f$. Here we prove uniqueness, thereby obtaining Fischer decompositions, under conditions that sometimes match those required for existence, and sometimes are more restrictive, depending on the parameters involved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_10419 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fischer decompositions for entire functions of sufficiently low order Aldaz, J. M. Render, H. Analysis of PDEs The existence of decompositions of the form $f=P\cdot q+r$ with $P_k^{\ast}\left( D\right) r=0$, where $f$ is entire, $P$ a polynomial and $P^{\ast}_k$ the principal part of $P$ with its coefficients conjugated, was achieved in \cite{AlRe23} under certain restrictions on the order of $f$. Here we prove uniqueness, thereby obtaining Fischer decompositions, under conditions that sometimes match those required for existence, and sometimes are more restrictive, depending on the parameters involved. |
| title | Fischer decompositions for entire functions of sufficiently low order |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2403.10419 |