Discrete and Continuous Signals: Analysis, Information and Applications

Integral formulas and inequalities for meromorphic functions and differences of subharmonic functions with applications

12 Dec 2023, 16:50

35m

St. Petersburg University, MCS faculty

Speakers

Bulat Khabibullin (Ufa Institute of Mathematics with Computing Centre) Enzhe Menshikova (Ufa Institute of Mathematics with Computing Centre)

Description

We consider various formulas relating integrals of delta-subharmonic functions to their Riesz distributions of charges.
These new formulas represent far-reaching developments and generalizations of the classical Poisson--Jensen, Shimizu--Ahlfors, I.I. Privalov, T. Carleman, B.Ya. Levin and other integral formulas.
A distinctive feature of the new formulas is the absence in them of any derivatives or function values at individual points.
The inequalities obtained from these formulas will be applied to uniqueness theorems for entire functions, to approximation in spaces of functions on subsets of the complex plane, etc. We will also indicate possible multidimensional complex generalizations of these results.