Carleman’s Formula for $$\boldsymbol{A(z)}$$-Analytic Functions
N. M. ZhabborovDepartment of Applied Mathematics of Tashkent State University of Economics, 100066, Tashkent, UzbekistanNurbek Kh. NarzillaevFaculty of Mathematics of the National University of Uzbekistan, 100174, Tashkent, UzbekistanBehzod HusenovDepartment of Mathematical Analysis of Bukhara State University, 200118, Bukhara, Uzbekistan
ABI
Abstract
In this paper, we investigate $$A(z)$$ -analytic functions, where $$A(z)$$ is a function that is antianalytic. The article demonstrates the existence of an $$A(z)$$ -harmonic measure at most points on the boundary of a lemniscate. The main contribution of this paper is the development of a new quenching function for $$A(z)$$ -analytic functions. This quenching function is used to derive Carleman formula for $$A(z)$$ -analytic functions in the Hardy class.
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