20.500.12556/RUL-154157 Reševanje nehomogene Cauchy-Riemannove enačbe s Hörmanderjevo metodo magistrsko delo Solving the nonhomogeneus Cauchy-Riemann equation by Hörmander's method Na začetku dvajsetega stoletja je bila klasifikacija domen holomorfnosti v ${\mathbb C}^n$ zelo pomembno vprašanje za kompleksno analizo več spremenljivk. Znano je bilo, da so domene holomorfnosti psevdokonveksne, obrat pa je postal znan kot Levijev problem. Na sredini dvajsetega stoletja je Oka prvi rešil Levijev problem in tako pokazal, da so domene holomorfnosti natanko psevdokonveksne domene. V desetletjih za tem so se razvile različne metode za preučevanje Levijevega problema. V tej magistrski nalogi se bomo osredotočili na metodo parcialnih diferencialnih enačb za reševanje nehomogene Cauchy-Riemannove enačbe, ki jo je razvil Hörmander. At the beginning of the twentieth century, a major question of several complex variables was the classification of domains of holomorphy. It was known that the domains of holomorphy were pseudoconvex; the converse however, became known as the Levi problem. In the middle of the twentieth century Oka first solved the problem and therefore showed that the domains of holomorphy were precisely the pseudoconvex domains. In the decades following this result, many different methods of studying the Levi problem were developed. In this thesis, we focus on the method of partial differential equations for solving the nonhomogeneous Cauchy-Riemann equation developed by Hörmander. Levijev problem nehomogena Cauchy-Riemannova enačba Hartogsov izrek Levi problem nonhomogeneus Cauchy-Riemann equation Hartogs theorem true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2024-01-28 07:15:09 2024-01-28 07:15:15 2024-05-29 09:49:08 0000-00-00 00:00:00 2024 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.5 139698 179484163 10893.pdf 10893.pdf 1 D2B070599EA93127E21B134CF0492BA3 530ebda730c6089e6a62306541c2e2e51ed85c0e4dc15bd14767e4a99dc950b8 9e454d85-bda4-11ee-a909-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=180364 Fakulteta za matematiko in fiziko 0 0 0