An extension of the Liouville theorem for Fourier multipliers to sub-exponentially growing solutions
David Berger
TU Dresden, Dresden, GermanyRené L. Schilling
TU Dresden, Dresden, GermanyEugene Shargorodsky
King’s College London, London, UKTeo Sharia
Royal Holloway University of London, Egham, Surrey, UK
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Abstract
We study the equation in a large class of sub-exponentially growing functions. Under appropriate restrictions on , we show that every such solution can be analytically continued to a sub-exponentially growing entire function on if, and only if, for .
Cite this article
David Berger, René L. Schilling, Eugene Shargorodsky, Teo Sharia, An extension of the Liouville theorem for Fourier multipliers to sub-exponentially growing solutions. J. Spectr. Theory 14 (2024), no. 2, pp. 665–695
DOI 10.4171/JST/509