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Aug 26, 2023 at 21:22 comment added NancyBoy Ok, thank you :)
Aug 26, 2023 at 21:18 comment added Michał Jan Except for $\beta_0=f$ and an infinite family of akin trivial examples, I do not.
Aug 26, 2023 at 21:11 comment added NancyBoy But in Alexander spoke only about exponential. My question was about the existence of a such positive family function. Do you know for this more general case ?
Aug 26, 2023 at 21:10 vote accept NancyBoy
Aug 26, 2023 at 15:14 comment added Michał Jan If you want to allow for $\beta_k$ to depend on $f$, which is what I assume you mean, then I think @AlexandreEremenko's comment sums it up.
Aug 26, 2023 at 13:03 vote accept NancyBoy
Aug 26, 2023 at 21:10
Aug 26, 2023 at 13:03 comment added NancyBoy But here you adress only linear combination of $f$. What about other transformations ?
Aug 26, 2023 at 12:00 vote accept NancyBoy
Aug 26, 2023 at 13:02
Aug 26, 2023 at 12:00 comment added NancyBoy Thabk you very much Michal Jan !
Aug 26, 2023 at 11:20 history answered Michał Jan CC BY-SA 4.0