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SUMMARY:Semigroup properties for multi-dimensional fractional integral ope
 rators - Arran Fernandez (Eastern Mediterranean University)
DTSTART:20220411T080000Z
DTEND:20220411T090000Z
UID:TALK170216@talks.cam.ac.uk
DESCRIPTION:One of the most commonly discussed properties for any fraction
 al differintegral operator is whether or not it has a semigroup property: 
 for example\, is the halfth integral of the halfth integral equal to the f
 irst integral? This question becomes more complicated in the setting of mu
 lti-parameter operators: for example\, the Prabhakar integrals have a semi
 group property in exactly two of their four parameters. We consider a gene
 ral multi-parameter fractional integral operator with a Fox-Wright kernel 
 function\, and catalogue exhaustively all possible subsets of its paramete
 rs in which a semigroup property is possible. This integral operator is in
  general multi-dimensional\, its dimension corresponding to the number of 
 gamma functions on the denominator of the Fox-Wright function. In the case
 s where a semigroup property holds\, we are able to construct a correspond
 ing multi-dimensional fractional derivative operator which has the same na
 tural inversion and analytic continuation properties as classical fraction
 al derivatives.
LOCATION:Seminar Room 2\, Newton Institute
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