Fourier transforms of bounded bilinear forms on \(C^*(S_{1})\times C^*(S_{2})\) of foundation \(*\)-semigroups \(S_{1}\) and \(S_{2}\)
A foundation semigroup is a locally compact topological semigroup which carries a suitable analogue of the group algebra \(L^1(G)\) of a locally compact group. In the paper under review the author introduces the \(C^*\)-algebra \(C^*(S)\) and the \(W^*\)-algebra \(W^*(S)\) of a foundation \(*\)-semigroup \(S\). Using these algebras, the author defines the Fourier transforms of bounded bilinear forms on \(C^*(S_1)\times C^*(S_2)\) of two foundation semigroups \(S_1\) and \(S_2\), and gives a characterization of these Fourier transforms in terms of Jordan \(*\)-representations, hemihomogeneous random fields, and weakly harmonizable random fields of \(S_1\) and \(S_2\) into the Hilbert space.
scientific article; zbMATH DE number 5323393
scientific article