CARLEMAN’S FORMULA FOR SKEW-SYMMETRIC MATRICES

Abstract

In this work, an integral formula in a matrix polydisk is obtained that allows one to recover the value of a function from the Hardy class at any internal point of the matrix polydisk from its values on part of the skeleton. All evidence presented is valid only if it mis even.

PDF

References

. Aizenberg L.A. Carleman’s formula in complex analysis. Novosibirsk: Nauka, 1990. –248 p (in Russian).

. Aizenberg L.A., Kytmanov A.M. On the possibility of holomorphic continuation into the domain of functions defined on a connected piece of the boundary // Mat. Sat. –1991. – T.182, No. 4. –P.490–508 (in Russian).

. Aizenberg L.A., Yuzhakov A.P. Integral representations and residues in multidimensional complex analysis. – Novosibirsk : Nauka, 1979. – 366 p (in Russian).

. Bellman R. Introduction to matrix theory. – M.: Nauka, 1976. – 368 p (in Russian).

. Vladimirov V.S. Methods of functions of several complex variables. M.: Nauka, 1964. –412 p (in Russian).

. Kosbergenov S. On Morera’s boundary theorem for a matrix ball // News of universities. Mathematics. – 2001. – No. 4(467). – pp. 28–32.

. Kytmanov A.M., Nikitina T.N. Analogues of Carleman's formula for classical domains // Mat. notes, –1989. T.45, No. 3, –P.87-93 (in Russian).

. Nathanson I.P. Theory of functions of a real variable. –M.: Nauka, 1974. –480 p (in Russian).

. Hua Lo - ken . Harmonic analysis of functions of many complex variables in classical domains. - M. , Ed . foreign lit., 1959. –163 with (in Russian).

. Khudayberganov G., Matyakubov Z.K., Carleman's formula for matrix upper half -planes // Acta NUUz , 2018, No. 2.1, pp. 8-14.

. Shaimkulov B. A. , Bozorov J.T., Carleman's Formula for a Matrix Polydisk //Journal of Siberian Federal University. Mathematics Physics . –2015. No8( 2). –P.371-374.

. U.S.Rakhmonov, Z.K.Matyakubov, Carleman's formula for the matrix domains of Siegel. Chebishevskiy sbornik , 2022 Vol. 23.No. 4. DOI 10.22405/2226-8383-2022-23-4-126-135.