A class of topological semigroups called GZH-semigroups is introduced. Conditions under which they have the property that limits of infinitesimal arrays are infinitely divisible are obtained. The convolution semigroup of all probability measures on a second countable LCA-group or on a real separable Hilbert space as well as the semigroup of all positive definite kernels defined on a countable set with complex values and with norms not greater than 1 are reduced to an extended form of Delphic semigroups.
"Central Limit Properties of GZH-Semigroups and Their Applications in Probability Theory." Ann. Probab. 21 (1) 185 - 201, January, 1993. https://doi.org/10.1214/aop/1176989400