Тип публикации: статья из журнала
Год издания: 2025
Идентификатор DOI: 10.33048/semi.2025.22.049
Ключевые слова: integral representations of Cauchy-Fantappié and Bochner-Martinelli, fundamental solution of the Laplace equation, holomorphic continuation, eigenfunctions and eigenvalues
Аннотация: Let D be a bounded domain in Cn (n>1) with a connected infinitely smooth boundary Γ , and the function f is harmonic in D and of class C1(D¯) . For a vector field w (not lying in the complex tangent plane to Γ) the differential ondition¯(f)=∑k=1nw¯k∂f∂z¯k=0 by Γ is considered. Will f be holomorphic in D? This problem is an analogueПоказать полностьюof the problem with an oblique derivative for real-valued harmonic functions. The paper shows that this problem is connected with a certain Cauchy-Fantappié integral representation Q , the kernel of which consists of derivatives of the fundamental solution of the Laplace equation. Under some additional conditions on the vector field w, it is shown that the iterations of Qm of this Cauchy-Fantappié integral representation converge to a holomorphic function. By doing so the problem under consideration has a positive reply.
Журнал: Сибирские электронные математические известия
Выпуск журнала: Т. 22, № 1
Номера страниц: 751-775
ISSN журнала: 18133304
Место издания: Новосибирск
Издатель: Институт математики им. С.Л. Соболева СО РАН