Let \(Q\) be a separable metric complete space with a Borel probability measure \(\rho\). The author treats here generalized translation operators, i.e. a family \(\{T_x\}\) of linear operators possessing the properties: \(\forall f\in C(Q)\), \(T_xf(y)= T_yf(x)\), \(x,y\in Q\), \(T_e= \text{id}.\), locality, and continuity. Character \(\chi(x,\lambda)\), \(\lambda\in N_0\) is \(0\not\equiv \chi\in C(Q)\) satisfying \(T_x\chi(y)= \chi(x)\cdot\chi(y)\), \(\chi(x,0)= 1\), where \(N_0\): a complex Hilbert space in a chain by \((N_p, N_{-p})\). Delsarte characters: \(\chi(x,\lambda)= \sum_{n=0\sim\infty}\langle \lambda^{\otimes n},\chi_n(x)\rangle\), and Appel characters: \(\sigma(x,\lambda)= \chi(x,\lambda)/\langle\langle\ell, \overline{\chi(\cdot,\lambda)}\rangle\rangle= \sum_{n= 0\sim\infty} \langle\lambda^{\otimes n}, P_n(x)\rangle/n!\). He gives Delsarte spaces \(H^\chi(p,q)\), \(H^x(-p,-q)= (H^\chi(p,q))'\) and Appel spaces \(H^P(p,q)\), \(H^P(-p,-q)\) as follows: \(\phi^n(x)= \langle\chi_n(x), a^n\rangle\), \(a^n\in N_p^{\widehat\otimes n}\), \(H^\chi(p,q)= \left\{\sum_{n= 0\sim\infty} \phi^n(x); \sum_{n= 0\sim\infty}\|\phi^n\|^2\cdot(n!)^2\cdot K^{qn}< \infty\right\}\). Appel characters turn into Delsarte characters by C-transform. Appel (Delsarte) cocharacters turn into powers by S-Tr. (T-Tr.). \(S\xi(\lambda)= \int\overline{\sigma(x, \overline\lambda)}\cdot\xi(x) d\rho(x)= \sum_{n= 0\sim\infty}\langle \lambda^{\otimes n}, \alpha^n\rangle\), \(\xi\in H^P(- p,-q)\). Wick product is also given by \(S^{-1}(S\xi(\lambda)\cdot S\eta(\lambda))\).