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

Eugene Shargorodsky, David Berger, René L. Schilling, Teo Sharia

Research output: Contribution to journalArticlepeer-review

Abstract

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
Pages (from-to)665-695
Number of pages30
JournalJournal of Spectral Theory
Volume14
Publication statusPublished - 13 Jun 2024

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