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* The [[absolute value]] function when defined on the set of real numbers or complex numbers is not everywhere analytic because it is not differentiable at 0. [[Piecewise|Piecewise defined]] functions (functions given by different formulae in different regions) are typically not analytic where the pieces meet.
* The [[complex conjugate]] function ''z'' → ''z''* is not complex analytic, although its restriction to the real line is the identity function and therefore real analytic, and it is real analytic as a function from <math>\mathbb{R}^{2}</math> to <math>\mathbb{R}^{2}</math>.
* Other [[non-analytic smooth function]]s, and in particular any smooth function <math>f</math> with compact support, i.e. <math>f \in C^\infty_0(\R^n)</math>, cannot be analytic on <math>\R^n</math>.<ref>{{Cite book|last=Strichartz, Robert S.|url=https://www.worldcat.org/oclc/28890674|title=A guide to distribution theory and Fourier transforms|date=1994|publisher=CRC Press|isbn=0-8493-8273-4|___location=Boca Raton|oclc=28890674}}</ref>
==Alternative characterizations==
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