Interesting Open Problem Related to Complexity of Computing the Fourier Transform and Group Theory

Nir Ailon

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arXiv · 1907.07471

Interesting Open Problem Related to Complexity of Computing the Fourier Transform and Group Theory

Nir Ailon

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Abstract

The Fourier Transform is one of the most important linear transformations used in science and engineering. Cooley and Tukey's Fast Fourier Transform (FFT) from 1964 is a method for computing this transformation in time $O(n\log n)$. From a lower bound perspective, relatively little is known. Ailon shows in 2013 an $\Omega(n\log n)$ bound for computing the normalized Fourier Transform assuming only unitary operations on pairs of coordinates is allowed. The goal of this document is to describe a natural open problem that arises from this work, which is related to group theory, and in particular to representation theory.

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Nir Ailon. 2019-07-17. Interesting Open Problem Related to Complexity of Computing the Fourier Transform and Group Theory. https://arxiv.org/abs/1907.07471

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