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Parametric operator

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A parametric operator Ω {\displaystyle \Omega \!} {\displaystyle \Omega \!} with parameter α {\displaystyle \alpha \!} {\displaystyle \alpha \!} in the parameter set A {\displaystyle \mathrm {A} \!} {\displaystyle \mathrm {A} \!} is an indexed family of operators ( Ω α ) A = { Ω α : α A } {\displaystyle (\Omega _{\alpha })_{\mathrm {A} }=\{\Omega _{\alpha }:\alpha \in \mathrm {A} \}\!} {\displaystyle (\Omega _{\alpha })_{\mathrm {A} }=\{\Omega _{\alpha }:\alpha \in \mathrm {A} \}\!} with index α {\displaystyle \alpha \!} {\displaystyle \alpha \!} in the index set A . {\displaystyle \mathrm {A} .\!} {\displaystyle \mathrm {A} .\!}

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