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April 2020 Fourier transforms, fractional derivatives, and a little bit of quantum mechanics
Fabio Bagarello
Rocky Mountain J. Math. 50(2): 415-428 (April 2020). DOI: 10.1216/rmj.2020.50.415

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 𝒮 ( ) , and then we extend it to its dual set, 𝒮 ( ) , 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. "Fourier transforms, fractional derivatives, and a little bit of quantum mechanics." Rocky Mountain J. Math. 50 (2) 415 - 428, April 2020. https://doi.org/10.1216/rmj.2020.50.415

Information

Received: 25 October 2019; Accepted: 3 December 2019; Published: April 2020
First available in Project Euclid: 29 May 2020

zbMATH: 07210968
MathSciNet: MR4104383
Digital Object Identifier: 10.1216/rmj.2020.50.415

Subjects:
Primary: 46N50

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 2 • April 2020
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