Definition 32.3.1 (Positive Linear Functional).label Let $G$ be a locally compact group and $\phi \in L^{1}(G; \complex)^{*}$[1], then $\phi$ is positive if $\dpn{f^* * f, \phi}{L^1(G; \complex)}\ge 0$ for all $f \in L^{1}(G)$.
- Due to technical difficulties, positive linear functionals are a priori not represented by $L^{\infty}$ functions. keyboard_return
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