01/19/2023, 06:41 PM
Just a thought.
it can be extended to the family of schroder function by
\[\sigma_f(z) = \int_{\mathbb{R}}{h(k)g(f^k(z))\mathrm{d}k}\] (and thus on measurable set in the way that k has some kinda shift-invariance), where \(h\) is any function that fits \(h(k-1)=s\,h(k)\), \(s\) is the multiplier, and \(g\) is any function.
it can be extended to the family of schroder function by
\[\sigma_f(z) = \int_{\mathbb{R}}{h(k)g(f^k(z))\mathrm{d}k}\] (and thus on measurable set in the way that k has some kinda shift-invariance), where \(h\) is any function that fits \(h(k-1)=s\,h(k)\), \(s\) is the multiplier, and \(g\) is any function.
Regards, Leo 