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

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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