Density of some systems of functions, quasianalyticity and subharmonic majorants

This work is concerned with density of some rather common classes of entire functions (for example, with density of the class of all entire functions of order less than $\sigma$) in $\Phi$-spaces. One of the typical examples of а $\Phi$-space is $C(E)$, where $E$ is a closed subset of $\mathbb{R}$. The dual problems reduce to questions concerning the quasianalyticity of classes of functions with Fourier transforms supported on a thin set. The latter problems are treated as problems of potential theory. Conformal mappings of the upper-half plane to special "comb-like" domains are systematically used.