Uniqueness sets with angular density for spaces of entire functions, I. Basics

This is the first part of our work which is devoted to the uniqueness sets for spaces of entire functions. In this part we consider a set $\mathrm{\Lambda }$ with angular density with respect to the order $\rho >0,$ satisfying the Lindelöf condition. We find the value of the critical zero set type for $\mathrm{\Lambda }$ in geometrical terms. We give a necessary and sufficient condition for the coincidence of the critical zero set type and the critical uniqueness set type. At the end of the paper we present an application of our results to random zero sets in Fock-type spaces.