6533b7ddfe1ef96bd127492b
RESEARCH PRODUCT
FOURIER TRANSFORMS, FRACTIONAL DERIVATIVES, AND A LITTLE BIT OF QUANTUM MECHANICS
Fabio Bagarellosubject
Pure mathematicsfractional derivativesGeneral MathematicsMathematical propertiesFOS: Physical sciencesContext (language use)Mathematical Physics (math-ph)Action (physics)Fractional calculusFourier transformsSet (abstract data type)symbols.namesakeFourier transformfractional momentum operatorDual basissymbols46N50QuantumMathematical PhysicsMathematicsdescription
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 $\Sc(\mathbb R)$, and then we extend it to its dual set, $\Sc'(\mathbb R)$, 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2020-04-01 |