Induced representations of hypergroups and positive definite measures (Q2704626)

A bounded regular Borel measure \(\mu\) on a hypergroup \(K\) is called (B)-positive definite if for any continuous complex-valued functions \(f,g\) on \(K\) with compact supports NEWLINE\[NEWLINE \int_K\overline f*f d\mu \geq 0,\quad \int_K\overline f*\overline g*g*f d\mu\leq \|g\|_1^2\int_K\overline f*f d\mu . NEWLINE\]NEWLINE NEWLINENEWLINENEWLINELet \(H\) be a closed subhypergroup of \(K\). It is shown that a (B)-positive definite measure \(\mu\) on \(H\) can be extended to a (B)-positive definite measure on \(K\) if and only if the corresponding representation \(T^{(\mu)}\) of \(H\) induces a representation of \(K\).