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In the book by Antosik, Mikusiński and Sikorski named Theory of Distributions, The Sequential Approach (russian translation, page 217) one can read:

Таким образом, мы видим, что для произвольного положительного целого числа $n$ не составляет труда построить преобразование $G$ простраства обобщенних функций медленного роста, такое, что $G^n=I$ (преобразование Фурье - Мелера).


Thus we see that it is not difficult to construct a transform $G$ of the tempered distribution space for which $G^n=I$ for an arbitrary positive integer $n$ (Fourier-Möller(?) transform).

This seems like a definition of Fractional Fourier Transform (the name itself wasn't around in the seventies, when the book was written). My question is: who is Möller (or is it Müller)? Papers on fractional FT don't seem to mention anyone with a similar surname.

Anyone with the English copy of this book could at least confirm the spelling.

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up vote 4 down vote accepted

Google "Fourier-Mehler transform"

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... and suddenly - that makes perfect sense. Thank you! – Harun Šiljak Aug 21 '12 at 15:58

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