TY - JOUR

T1 - FOURIER TRANSFORMS, FRACTIONAL DERIVATIVES, AND A LITTLE BIT OF QUANTUM MECHANICS

AU - Bagarello, Fabio

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Fourier transforms

KW - fractional derivatives

KW - fractional momentum operator

KW - Fourier transforms

KW - fractional derivatives

KW - fractional momentum operator

UR - http://hdl.handle.net/10447/424989

UR - https://arxiv.org/pdf/1912.01836.pdf

M3 - Article

VL - 50

SP - 415

EP - 428

JO - Rocky Mountain Journal of Mathematics

JF - Rocky Mountain Journal of Mathematics

SN - 0035-7596

ER -