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Is there exact formula that returns minimal period of a periodic analytic function? For constant it should return 0, for non-periodic functions - infinity.

I only came to the following but it requires taking the smallest branch of a multivalued function. I would like an answer not involving multi-valued functions.

$$T[f]=\left(\int_{-\infty}^{+\infty}|f(s+t)-f(s)|ds\right)^{[-1]}|_{t=0}$$

Anixx
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    Not all functions have a minimal period: Consider the characteristic function $\chi_{\mathbb Q}: \mathbb{R} \to \mathbb{R}$ of the rational numbers. – Travis Willse Nov 19 '14 at 14:34
  • What is "inexact" in the term "minimal period"? Why not just use that? Or will you restrict what you mean by "exact formula"? – GEdgar Nov 19 '14 at 14:35
  • @Travis for such functions the formula ideally would return $0$ like for constants. But I would be satisfied if the formula worked for only analytic functions. – Anixx Nov 19 '14 at 14:36
  • @GEdgar I want a formula(expression) representation, that would give it for arbitrary analytic function. Like a limit, series, integral, sum etc. – Anixx Nov 19 '14 at 14:37
  • I suppose what you're looking for is a function that returns the infimum of all of the periods. – Travis Willse Nov 19 '14 at 14:42
  • @Travis yes, infimum of all positive periods. Ideally. But if it worked only for non-constant analytic functions, it would be ok. – Anixx Nov 19 '14 at 14:44

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