An extension of the Liouville theorem for Fourier multipliers to sub-exponentially growing solutions

Teo Sharia, Eugene Shargorodsky, David Berger, Rene Shilling

Research output: Contribution to journalArticlepeer-review


We study the equation $m(D)f=0$ in a large class of sub-exponentially growing functions. Under appropriate restrictions on $m \in C(\real^n)$ we show that every such solution can be analytically continued to a sub-exponentially growing entire function on $\comp^n$ if, and only if, $m(\xi) \neq 0$ for $\xi \neq 0$.
Original languageEnglish
Number of pages30
JournalJournal of Spectral Theory
Publication statusAccepted/In press - 1 Mar 2024

Cite this