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    STUDIA MATHEMATICA - Issue no. 2 / 2011  
         
  Article:   ITERATES OF MULTIDIMENSIONAL KANTOROVICHTYPE OPERATORS AND THEIR ASSOCIATED POSITIVE C0-SEMIGROUPS.

Authors:  .
 
       
         
  Abstract:  

In this paper we deepen the study of a sequence of positive linear operators acting on L1([0, 1]N), N 1, that have been introduced in [3] and that generalize the multidimensional Kantorovich operators (see [15]). We show that particular iterates of these operators converge on C ([0, 1]N) to a Markov semigroup and on Lp([0, 1]N), 1 p < +, to a positive contractive C0-semigroup (that is an extension of the previous one). The generators of these C0-semigroups are the closures of some partial differential operators that belong to the class of Fleming-Viot operators arising in population genetics.

 

Mathematics Subject Classification (2010): 41A36, 47D06, 47F05.

 

Keywords: Multidimensional Kantorovich operator, positive approximation process, iterate of operators, positive C0-semigroup, approximation of semigroups, Fleming-Viot operator

 
         
     
         
         
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