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Is it possible to define the Mellin transform for sequences of real numbers or even for tuples? Is there any book treating this argument?

Any idea or suggestion will be greatly appreciated

Since the suggestions are very promising I edited the question to add some details:

Is there a natural way to define a discrete Mellin transform in the same way discrete Fourier transform is defined (look for example to https://en.wikipedia.org/wiki/Discrete_Fourier_transform) . How is defined and what are its properties? I'm not able to see this kind of construction (if possible) in the suggested texts.

The question arose me looking at Variations on the Mellin and Dirichlet transforms but the proposed paper is in russian and I'm looking for a more "user friendly" introductory text beside the fact I'm not able to understand Russian.

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Yes, the Discrete Mellin Transform has been developed. The approach is detailed in the paper by Bertrand et al available here

See chapter 3, especially section 3.3

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    $\begingroup$ that's the paper I cited in the comment right? I am not sure that this applies to "a sequence of real numbers". $\endgroup$
    – Carlo Beenakker
    Commented Jun 5, 2022 at 13:42
  • $\begingroup$ we must have been typing at the same time. let's see what the OP says. $\endgroup$
    – kodlu
    Commented Jun 5, 2022 at 17:54

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