... deLyra¹

Email: delyra@latt.if.usp.br

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... integral²

Post-publication note: it is important to observe here that, from its very beginning, this argument goes through without any change if we replace $u_{\gamma}(\rho,\theta)$ directly by $g(\theta)$ in the integrand. Hence, the theorem is true regardless of whether or not the real function $g(\theta)$ is represented by an inner analytic function.

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... limit³

Post-publication note: this characterizes the inner analytic function $w_{\delta}(z,z_{1})$ associated to the Dirac delta ``function'' as an irregular inner analytic function, since it is not integrable around its singular point, which is a hard singular point with degree of hardness $1$, while the corresponding real object is.

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... limit⁴

Post-publication note: this characterizes all the inner analytic functions $w_{\delta}^{n\mbox{\Large$\cdot$}\!}(z,z_{1})$ associated to the derivatives of the Dirac delta ``function'' as irregular inner analytic functions, since they are not integrable around their singular points, which are hard singular points with degrees of hardness $n+1$, while the corresponding real objects are.

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... circle⁵

Post-publication note: another way to state this is to say that the inner analytic functions associated to singular distributions must be irregular inner analytic functions, since they are not integrable around their singular points, which are hard singular points with strictly positive degrees of hardness, while the corresponding real objects are.

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