An extension of the Liouville theorem for Fourier multipliers to sub-exponentially growing solutions
Research output: Contribution to journal › Research article › Contributed › peer-review
Contributors
Abstract
We study the equation m(D)f D 0 in a large class of sub-exponentially growing functions. Under appropriate restrictions on m ∈ C(Rn), we show that every such solution can be analytically continued to a sub-exponentially growing entire function on Cn if, and only if, m(ζ) ≠ 0 for ζ ≠ 0.
Details
| Original language | English |
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| Pages (from-to) | 665-695 |
| Number of pages | 31 |
| Journal | Journal of Spectral Theory |
| Volume | 14 (2024) |
| Issue number | 2 |
| Publication status | Published - 30 May 2024 |
| Peer-reviewed | Yes |
External IDs
| Scopus | 85196307620 |
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Keywords
ASJC Scopus subject areas
Keywords
- Beurling-Domar condition, Fourier multipliers, Liouville theorem, entire functions