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Some general representation formulae for (C0)m-parameter operator semigroups with rates of convergence are obtained by the probabilistic approach and multiplier enlargement method. These cover all known representation formulae for (C0) oneand mparameter operator semigroups as special cases. When we consider special semigroups we recover well-known convergence theorems for multivariate approximation operators.

Representation formulae for (C₀) m-parameter operator semigroups