Abstract
We study the set of functions in quasi-analytic classes and the set of finely holomorphic functions. We show that no one of these two sets is contained in the other.
LetI denote the set of complex functionsf:ℝ → ℂ for which there exists a quasi-analytic classC{M n} containingf. Let ℱ denote the set of complex functionsf:ℝ → ℂ for which there exist a fine domainU containing the real line ℝ and a function\(\tilde f\) finely holomorphic onU satisfyingf(x)=\(\tilde f\)(x) for allx ∈ ℝ. The “power” of unique continuation is incomparable in these two cases (I\ℱ is non-empty, ℱ\I is non-empty).
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Research supported by the grant No. 201/93/2174 of Czech Grant Agency and by the grant No. 354 of Charles University.
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Pyrih, P. Finely holomorphic functions and quasi-analytic classes. Potential Anal 3, 273–281 (1994). https://doi.org/10.1007/BF01468247
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DOI: https://doi.org/10.1007/BF01468247