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

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

Research output: Working paper/PreprintPreprint

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Abstract

We study the equation m(D)ƒ=0 in a large class of sub-exponentially growing functions. Under appropriate restrictions on mC(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(ξ)≠0 for ξ≠0.
Original languageEnglish
PublisherarXiv
Number of pages25
DOIs
Publication statusPublished - 23 Jan 2024

Keywords

  • math.AP

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