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 -