REZOLVENTA

REZOLVENTA (az lotini gezo1uep-Iz — miftoq, girehkusho) dar matematika, muodila, funksiya (yadro) yo khud operatori miftohiero guyand, ki dar halli muodilahoi operatori istifoda meshavad. Dar algebra istilohi «Rezolventa» ba chand mani istifoda meshavad. Masalan, Rezolventai muodilai algebravii / (kh) = 0-i da-rajai p gufta, chunin muodilai algebravii £(kh) = 0-ro menomand, ki koeffisienthoyash ba koeffisienthoi 1(kh) ratsionali  vobastaand va donistani reshahoi on baroi yoftani reshahoi muodilai ](kh) = 0 im-kon medihad. Masalan, muodilai

V3 — av1>* + (a\a& — 4a4)i — (‘o,,a4 — — 4a2a4 + a%7) = 0

yake az R,-hoi kubii muodilai darz-jai chorumi kh4 + a,kh3 + az** + ozkh + 04 = 0     (1)meboshad. Agar i,, *>2, o$ reshahoi ii Rezolventa  boshand, on goh reshahoi *\, kh2, kh4-i muodilai (1) dar natijai hal kardani muodilahoi kvadratii a2 — + a4 = 0, k = 1, 2, 3 barovarda meshavand. Yane agar g)l reshahoi muodilahoi kvadrati boshand, kh,kh2 =     *z*4 == t)|. «1*3 = |g, Kh2Kh4 = T)2, *\*4 = YOz,       — T)3, “= ||^2/t)z va gayra meboshad. Dar naza-riyai muodilahon integrali RezolventaR.-i (yad-roi miftoh) muodilai F (•) + *(•, ShF Sh = !(•) (2) a gufta, funksiyai G(z, 1\ Kh)-«i az tagyiryobandahoi, I va parametri X vobastaro mefahmand, ki tavassuti on halli muodilai (2)-ro dar namudi / (•) + Ya. / R (•, <, X) ((() <I navishtan mumkin. Dar nazariyai operatorhoi khatti Rezolventai operatori A oilai operatorhoi = (L — KhE)-1 meboshad, ki dar on parametri kompleksii X hamai qimathoi ba spektri operatori A nomutaalliqro qabul karda metavonad.