Integral Formulas for Subharmonic and Meromorphic Functions and Completeness of Exponential Systems

We obtain new integral formulas for holomorphic, meromorphic, subharmonic and \(\delta\) -subharmonic functions on a concentric annulus. These formulas relate integrals from such functions to their distributions of zeros and poles, as well as Riesz measures and charges, respectively. Our new formulas are applied to obtaining inequalities for such functions and to new completeness conditions for exponential systems in Banach spaces of functions on a convex compact set in the complex plane.