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Have Feller semigroups been used to investigate the properties of the Cauchy problem associated with the fractional Laplacian (just like they have been used to study local degenerate second order equations)? Can you point out any references?

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  • $\begingroup$ What do you mean by "investigate the properties of the Cauchy problem associated with the fractional Laplacian"? Would you like to know whether the semigroup generated by fractional Laplacians is Feller? $\endgroup$ – Delio Mugnolo Feb 5 at 7:43
  • $\begingroup$ @DelioMugnolo Yes I'm interested in that too. Also if such semigroup is represented as iterates of a positive linear operator. $\endgroup$ – Dal Feb 5 at 10:24

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