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arXiv · 1912.01836

Fourier transforms, fractional derivatives, and a little bit of quantum mechanics

FAbio Bagarello
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Abstract

We discuss some of the mathematical properties of the fractional derivative defined by means of Fourier transforms. We first consider its action on the set of test functions $\Sc(\mathbb R)$, and then we extend it to its dual set, $\Sc'(\mathbb R)$, the set of tempered distributions, provided they satisfy some mild conditions. We discuss some examples, and we show how our definition can be used in a quantum mechanical context.

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FAbio Bagarello. 2019-12-04. Fourier transforms, fractional derivatives, and a little bit of quantum mechanics. https://arxiv.org/abs/1912.01836

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