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

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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 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.
Original languageEnglish
Pages (from-to)415-428
Number of pages14
JournalRocky Mountain Journal of Mathematics
Volume50
Publication statusPublished - 2020

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