BOUNDARY PAIRS ENSURING THE WELL-POSEDNESS OF OPERATORS GENERATED BY THE CAUCHY-RIEMANN DIFFERENTIAL OPERATOR

N. S. Imanbaev

2026

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DOI 10.17654/0972087126057

Data confidence 70 medium

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Abstract

We study the well-posedness of a spectral problem generated by the Cauchy-Riemann differential operator. Based on the author’s previous works, where the Dirichlet-type problem for the Cauchy-Riemann operator is studied and the Volterra nature of the original problem is established, boundary pairs are constructed for (i) a spectral problem with nonlocal boundary conditions and (ii) a spectral problem with Bitsadze-Samarskii-type boundary conditions. A boundary pair consists of a bounded linear operator mapping continuous functions in the unit disk to holomorphic functions and a bounded linear functional acting on continuous functions in the unit disk.