Carleman’s Integral Formula in Cartesian Product of Matrix Upper Half-Plane

Year 2024, Volume: 14 Issue: 2, 36 - 45, 31.07.2024

Jonibek Sh. Abdullayev Kudrat Sh. Ruzmetov Zokirbek K. Matyakubov

Abstract

Carleman’s formulas solve the problem of recovery of a function from such
a class of its values on the set of uniqueness M ⊂ ∂D for this class that does not
contain the Shilov boundary ∂D. In this paper, by using the matrix upper half-plane
and the biholomorphic equivalence of the matrix unit disc, the Carleman formula for the
Cartesian product of matrix upper half-planes is proved

Keywords

matrix unit disc, automorphism, holomorphic function, Cauchy-Szeg˝o’s kernel, Carleman‘s formulas, Cartesian product.

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