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The Bochner—Martinelli integral operator for real analytic functions
https://doi.org/10.26907/0021-3446-2025-7-53-63
Abstract
Let D be a bounded domain in Cn (n > 1) with a real analytic connected boundary dD = Г. The Bochner-Martinelli integral (integral operator) M(f) is considered for real analytic functions f о n Г. It is shown th at the integral M (f) is real analytic up to Г. Iterations of the Bochner-Martinelli integral Mk(f) are considered. It is proved that they converge to a function holomorphic in D at k ^ to. The Bochner-Маrtinelli transform M(T)(z) is defined for analytical functionals T. It is proved that the iterations of Mk(T)(z) converge weakly to a CR-functional at k ^ to.
About the Authors
A. M. Kytmanov
Siberian Federal University
Russian Federation
Russian Federation
Alexander Mechislavovich Kytmanov
79 Svobodny Ave.; Krasnoyarsk; 660041
S. G. Myslivets
Siberian Federal University
Russian Federation
Russian Federation
Simona Glebovna Myslivets
79 Svobodny Ave.; Krasnoyarsk; 660041
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Review
For citations:
Kytmanov A.M., Myslivets S.G. The Bochner—Martinelli integral operator for real analytic functions. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika. 2025;(7):53-63. (In Russ.) https://doi.org/10.26907/0021-3446-2025-7-53-63
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