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 i(R), and then we extend it to its dual set, i'(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.

Bagarello, F. (2020). FOURIER TRANSFORMS, FRACTIONAL DERIVATIVES, AND A LITTLE BIT OF QUANTUM MECHANICS. ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 50(2), 415-428 [10.1216/rmj.2020.50.415].

FOURIER TRANSFORMS, FRACTIONAL DERIVATIVES, AND A LITTLE BIT OF QUANTUM MECHANICS

Bagarello, F
2020

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 i(R), and then we extend it to its dual set, i'(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.
https://arxiv.org/pdf/1912.01836.pdf
Bagarello, F. (2020). FOURIER TRANSFORMS, FRACTIONAL DERIVATIVES, AND A LITTLE BIT OF QUANTUM MECHANICS. ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 50(2), 415-428 [10.1216/rmj.2020.50.415].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/424989
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