Definition:Parametric Operator

A parametric operator $$\Omega\!$$ with parameter $$\alpha\!$$ in the parameter set $$\Alpha\!$$ is an indexed family of operators $$(\Omega_{\alpha})_{\Alpha} = \{\Omega_{\alpha} : \alpha \in \Alpha\}$$ with index $$\alpha\!$$ in the index set $$\Alpha\!$$.