Teorema Hartogsa tverdzhennya u kompleksnomu analizi pro te sho u vipadku koli kompleksna funkciya bagatoh kompleksnih zminnih bude analitichnoyu za kozhnim zi svoyih argumentiv to vona takozh bude analitichnoyu zagalom Tverdzhennya RedaguvatiNehaj W C n displaystyle Omega subseteq mathbb C n nbsp vidkrita mnozhina a 1 a n C displaystyle a 1 dots a n in mathbb C nbsp deyaki chisla Poznachimo W j a z C a 1 a j 1 z a j 1 a n W C displaystyle Omega j a left z in mathbb C a 1 dots a j 1 z a j 1 dots a n in Omega right subseteq mathbb C nbsp Dlya funkciyi f W C displaystyle f Omega rightarrow mathbb C nbsp mozhna viznachiti funkciyi f j a W j a C displaystyle f j a Omega j a rightarrow mathbb C nbsp diya yakih viznachayetsya z f a 1 a j 1 z a j 1 a n displaystyle z mapsto f a 1 dots a j 1 z a j 1 dots a n nbsp Pri cih poznachennyah yaksho a 1 a n C j N 1 j n displaystyle forall a 1 dots a n in mathbb C forall j in mathbb N 1 leq j leq n nbsp funkciyi f j a W j a C displaystyle f j a Omega j a rightarrow mathbb C nbsp ye analitichnimi to i funkciya f W C displaystyle f Omega rightarrow mathbb C nbsp ye analitichnoyu Div takozh RedaguvatiLema OsgudaLiteratura RedaguvatiSteven G Krantz Function Theory of Several Complex Variables AMS Chelsea Publishing Providence Rhode Island 1992 Otrimano z https uk wikipedia org w index php title Teorema Hartogsa amp oldid 38063610
