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SUMMARY:On fractional Wirtinger derivatives for complex analysis - Arran F
 ernandez (Eastern Mediterranean University)
DTSTART:20220131T140000Z
DTEND:20220131T150000Z
UID:TALK169394@talks.cam.ac.uk
DESCRIPTION:Despite its importance in mathematics\, complex analysis is a 
 field which has not been much explored from the fractional viewpoint. Comp
 lex-order fractional differintegrals are well known\; fractional differint
 egrals of complex functions are also fairly standard\; but many of the spe
 cialised facts and operations of complex analysis have had no fractional a
 nalogues. We consider the Wirtinger derivatives (in particular\, the compl
 ex d-bar derivative) and how to define fractional versions of these operat
 ors. To motivate and justify the definitions\, we compare their properties
  both with the original d-bar and Wirtinger derivatives and with the origi
 nal fractional calculus\, noting that the natural analogues emerge as expe
 cted. Potential applications will also be discussed. Joint work with Chaim
 a Bouzouina.
LOCATION:Seminar Room 2\, Newton Institute
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