Mathematics

Generalized Carleman formula for semiring and semidisc

K. G. Malyutin, A. A. Naumova

Kursk State University, Kursk, Russia

Abstract: A generalization of the Carleman formula for the subharmonic function in an open semiring and in an open semidisc is obtained. The generalized formula takes into account both the distribution of the Riesz measure of the function and its boundary measure. The proof uses the theory of thin topology and Martin spaces.

Keywords: Carleman formula, semiring, semicircle, subharmonic function, Riesz measure, boundary measure, full measure.

UDC: 517.53

Received: 30.01.2025
Revised: 09.08.2025

DOI: 10.47475/2500-0101-2025-10-4-688-700