Eurasian Journal of Mathematical Theory and Computer Sciences 6-jild 8-son (2026) · 12–21-betlar

CONVERGENCE DOMAIN OF SERIES OF HOLOMORPHIC FUNCTIONS AND PROBLEMS OF ANALYTIC CONTINUATION

Safarboyeva, Gulhayo

DOI: 10.70413/ejmtcs-v06-i08-p1-002 · Manbada o'qish → · PDF (manba serverida)

Annotatsiya

The paper examines the relationship between the convergence domain of a series of holomorphic functions and the domain of holomorphy of its sum - a question resolved differently in one- and several-variable complex analysis. Classical tools (Cauchy-Hadamard formula, Weierstrass and Abel theorems, Hadamard's gap criterion) are combined with the Hartogs extension theorem and plurisubharmonic function techniques. Using an original computed example, it is shown that the convergence domain of a multiple power series can never coincide with a Hartogs figure - it always automatically fills out to a complete, logarithmically convex Reinhardt domain, consistent with and verified against the Hartogs extension theorem. A fundamental qualitative difference between the one- and several-variable settings regarding natural boundaries is demonstrated.

Holomorphic function, functional series, convergence domain, analytic continuation, Hartogs phenomenon, domain of holomorphy.Голоморфная функция, функциональный ряд, область сходимости, аналитическое продолжение, явление Хартогса, область голоморфности.Golomorf funksiya, funksional qator, yaqinlashish radiusi, yaqinlashish sohasi, analitik davom ettirish, tabiiy chegara, Xartogs fenomeni, plyurisubgarmonik funksiya, golomorflik sohasi.

Metadata manbasi: jurnal OAI-PMH arxivi · Sindex to'liq matnni saqlamaydi, manbaga havola beradi.