sakaratmak harmonic karya

ganitamadhye, jatil sankhyanmadhil ekak discoveril sakaratmak harmonic karya heey vartulavaril maryadit sakaratmak mojamapache poison avibhajya mhanoon darshavile jaate. haah parinam, "herglotz-riz pratinidhitva pramey", 1911 madhye gustav herglotz aanee frigies riz yanni swatantrapane siddha kele. yacha vapar sakaratmak vastavik bhag asalelya unit discoveril konatyahi holomorphic karyasathi sambandhit sootra aanee vaishishtyikaran denyasathi keela jaau shakato. asha karyanche vaishishtya 1907 madhye tyanchya teller gunankanchya sakaratmak nishchitatechya drushtine sthirank caratheodoridware aadhich darshavile gele hote.
harmonic functionsasathi herglotz-riz pratinidhitva pramey.
jarr aanee keval jarr ekak vartulavar sambhavyateche mojmap asey asel qee, 'f' (0) = 1 asalele ekak discoveril sakaratmak karya 'f' heey susangat asel.
sootra spashtapane "f" (0) = 1 saha sakaratmak harmonic karya paribhashit karate.
yaulat jarr 'f' sakaratmak aanee harmonic asel aanee 'r' n '1 paryant vadhala tarr paribhashit qaraa.
mug
kuthe?
haah sambhavyatecha eka upay aahe.
sankshiptata yuktivadadvare (kinwa yaa prakaranat samatulya
steeltjes integralsasathi helinche nivad pramey), yaa sambhavyatechya upayanchya pudhil tappyat kamkuvat maryada asate jee sambhavyateche mojmap dekhil aahe.
r" "n" vadhoon 1 hott asalyane, tyamule "f" "n" ("z") chaa cull "f" ("z") assa hoto, herglotz sootra khalilpramane aahe ".
holomorphic functionsasathi herglotz-riz pratinidhitva pramey.
jarr aanee keval jarr ekak vartulavar sambhavyateche mojmap asey asel qee, jarr ekak discover 'f' (0) = 1 asalele 'f' heey samaroop karya asel, tarr tyacha vastavik bhag sakaratmak asel.
heey mageel prameyavarun yete karanah
holomorphic karyansathi caratheodoricha sakaratmak nikash.
jaau dya.
unit discover eka holomorphic karya asoo dya. mug 'f' ('z') chaa discover sakaratmak vastavik bhag asato.
jarr aanee fakt
konatyahi jatil sankhyansathi λ0, λ1,..., λ "n", kuthe
m"> 0 sathee.
kharey tarr 'aine'> 0 sathee herglotz pratinidhitvatun
tyamule
yaulat, λ "n" = "z" n "nishchit karane,

