About a conjecture on difference equations in quasianalytic Carleman classes
Keyword(s):
We consider the difference equation ?q j=1 aj (x)?(x+?j) = ?(x) where ?1 < ??? < ?q (q ? 3) are given real constants, aj(j=1,...,q) are given holomorphic functions on a strip R? (? > 0) such that a1 and aq vanish nowhere on it, and ? is a function belonging to a quasianalytic Carleman class CM{R}. We prove, under a growth condition on the functions aj, that the difference equation above is solvable in CM{R}.
2011 ◽
Vol 216
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pp. 50-55
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1999 ◽
Vol 09
(07)
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pp. 1285-1306
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2018 ◽
Vol 72
(1)
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pp. 19
2021 ◽
Vol 11
(1)
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pp. 68-74
Keyword(s):