Iterates of multidimensional Kantorovich-type operators and their associated positive \(C_0\)-semigroups (Q2891135)
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scientific article; zbMATH DE number 6045959
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Iterates of multidimensional Kantorovich-type operators and their associated positive \(C_0\)-semigroups |
scientific article; zbMATH DE number 6045959 |
Statements
13 June 2012
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multidimensional Kantorovich operator
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positive approximation process
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iterate of operators
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positive \(C_0\)-semigroup
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approximation of semigroups
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Fleming-Viot operator
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0.88794094
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0.8840267
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0.8805835
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0.8758044
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Iterates of multidimensional Kantorovich-type operators and their associated positive \(C_0\)-semigroups (English)
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The authors continue the study of the convergence of iterates of a class of positive linear operators defined on \(L^1[0,1]^n\). In the one dimensional case (i.e. \(n=1\)), these operators are reminiscent of subsequences of the Bernstein operators. The multidimensional version is more general than Kontorovich operators.NEWLINENEWLINE This work proves that when restricted to the continuous functions, the iterates of such operators converge and the convergents belong to a Markov semi-group. When the operators are defined on \(L^p[0,1]\) for \(1\leq p<\infty\), then the limits of the iterates belong to a positive, contractive \(C_0\)-semigroup.
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