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SUMMARY:The fractional Laplacian of a function with respect to another fun
 ction - Arran Fernandez (Eastern Mediterranean University)
DTSTART:20220222T090000Z
DTEND:20220222T093000Z
UID:TALK167678@talks.cam.ac.uk
DESCRIPTION:The fractional Laplacian is a widely used tool in multi-dimens
 ional fractional PDEs\, useful because of its natural relationship with th
 e multi-dimensional Fourier transform via fractional power functions. A we
 ll-known general class of fractional operators is given by fractional calc
 ulus with respect to functions\; this has usually been studied in 1 dimens
 ion\, but here we study how to extend it to an $n$-dimensional setting. We
  also formulate Fourier transforms with respect to functions\, both in 1 d
 imension and in $n$ dimensions. Armed with these building blocks\, it is p
 ossible to construct fractional Laplacians with respect to functions\, bot
 h in 1 dimension and in $n$ dimensions. These operators can then be used f
 or posing and solving some generalised families of fractional PDEs.\nJoint
  work with Joel E. Restrepo (Nazarbayev University) and Jean-Daniel Djida 
 (AIMS Cameroon).
LOCATION:Seminar Room 1\, Newton Institute
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