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

Research output: Contribution to journalResearch articleContributedpeer-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 languageEnglish
Pages (from-to)665-695
Number of pages31
JournalJournal of Spectral Theory
Volume14 (2024)
Issue number2
Publication statusPublished - 30 May 2024
Peer-reviewedYes

External IDs

Scopus 85196307620

Keywords

Keywords

  • Beurling-Domar condition, Fourier multipliers, Liouville theorem, entire functions