An extension of the Liouville theorem for Fourier multipliers to sub-exponentially growing solutions
| Autor: | Berger, David, Schilling, René L., Shargorodsky, Eugene, Sharia, Teo |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We study the equation $m(D)f = 0$ in a large class of sub-exponentially growing functions. Under appropriate restrictions on $m \in C(\mathbb{R}^n)$, we show that every such solution can be analytically continued to a sub-exponentially growing entire function on $\mathbb{C}^n$ if and only if $m(\xi) \not= 0$ for $\xi \not= 0$. |
| Databáze: | arXiv |
| Externí odkaz: |
|