fredgol‘mning aynigan yadroli integral tenglamalari

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1629116959.doc ) ( ) ( ) , ( ) ( x f dy y y x k x b a = - ò j l j ) , ( y x k å = = n i i i y q x p y x k 1 ) ( ) ( ) , ( ) ( x p i ) ( y q i b y a b x a £ £ £ £ , ) ( x p i ) ( y q i å ò = = - n i b a i i x f dy y y q x p x 1 ) ( ) ( ) ( ) ( ) ( j l j å = + = n i i i x p c x f x 1 ) ( ) ( ) ( l j n i dy y y q c b …

m k k ,....., 2 , 1 , = = l l ) ( x f r n j x j - = ,....., 2 , 1 ), ( y fredgol‘mning aynigan yadroli integral tenglamalari fredgol‘mning aynigan yadroli integral tenglamalari reja: 1. fredgol‘mning birinchi teoremasi. 2. fredgol‘mning ikkinchi teoremasi. 3. fredgol‘mning uchinchi teoremasi. 1. fredgol‘mning birinchi teoremasi. fredgol‘mning ikkinchi tur (1) integral tenglamasining yadrosi (2) ko‘rinishda bo‘lsa, u aynigan (buzilgan) yadro deb yuritiladi. bundagi va , -berilgan haqiqiy uzluksiz funksiyalardir. ayrim adabiyotlarda (2) ko‘rinishdagi yadro pinkerle-gursa yadrosi, yoki qisqacha pg-yadro deb ham ataladi. umumiylikka ziyon etkazmay, barcha funksiyalarni ham funksiyalarni ham o‘zaro bog’liq emas deb hisoblaymiz. aks holda (2) yig’indida qo‘shiluvchilar sonini kamaytirish mumkin. (2) ifodani (1) integral tenglamaga qo‘yib, (3) tenglamani hosil qilamiz. (3) integral tenglamani (4) ko‘rinishda yozish mumkin, bunda lar noma’lum funksiyaga bog’liq bo‘lgani uchun noma’lum o‘zgarmaslardir. endi o‘zgarmas sonlarni shunday tanlashga harakat qilamizki, natijada (4) fomula …

rosning yoki bunga mos (3) integral tenglamaning xos (xarakteristik) sonlari deyiladi. shunday qilib, ning lardan farqli bo‘lgan har bir chekli qiymat uchun (5) sistema yagona echimga ega bo‘ladi. bu echimni (4) tenglikning o‘ng tomoniga qo‘yib, (3) integral tenglamaning echimiga ega bo‘lamiz. natijada quyidagi teoremani isbotladik. fredgol’mning birinchi teoremasi. agar embed equation.3 yadroning xos soni bo‘lmasa, ixtiyoriy uzluksiz uchun (3) integral tenglama echimiga ega, shu bilan birga bu echimga yagona bo‘ladi. 2. fredgol‘mning ikkinchi teoremasi. (3) integral tenglamaga mos bir jinsli (7) tenglama (5) ga mos bo‘lgan ushbu (8) bir jinsli chiziqli algebik sistemsgs keladi. (7) tenglamaga qo‘shma bo‘lgan bir jinsli tenglama, (9) ko‘rinishga ega bo‘ladi. (9) tenglamaga ega (8) ga qo‘shma bo‘lgan bir jinsli sistemaga teng kuchlidir, bunda agar bo‘lib, matrisaning rangi ga teng bo‘lsa, chiziqli algebradan ma’lumki, bir jinsli (8) sistema ham va unga qo‘shma bo‘lgan (10) sistema ham ta chiziqli bog’liq bo‘lmagan echimlarga ega bo‘ladi. bu echimlarni (7) …

bo‘ladi. biror sohada, xususan oraliqda, ikkita funksiyaning ko‘paytmasidan olingan integral nolga teng bo‘lsa, bu funksiyalar ortogonal deb ataladi. shunday qilib biz quyidagi teoremani isbot qildik. fredgolmning uchunshi teoremasi. bo‘lganda (3) integral tenglamaning echimiga ega bo‘lishi uchun uning ozod hadi ning qo‘shma bir jinsli (8) tenglamaning barcha echimlariga ortogonal bo‘lishi zarur va etarlidir. _1073320619.unknown _1073320733.unknown _1073320790.unknown _1073323140.unknown _1073373783.unknown _1073401318.unknown _1073401467.unknown _1073401716.unknown _1073401805.unknown _1073401395.unknown _1073373942.unknown _1073324069.unknown _1073324239.unknown _1073324583.unknown _1073324722.unknown _1073324376.unknown _1073324173.unknown _1073323664.unknown _1073323804.unknown _1073323485.unknown _1073321464.unknown _1073321941.unknown _1073322949.unknown _1073321484.unknown _1073321239.unknown _1073321287.unknown _1073321206.unknown _1073320747.unknown _1073320769.unknown _1073320779.unknown _1073320758.unknown _1073320745.unknown _1073320746.unknown _1073320744.unknown _1073320695.unknown _1073320709.unknown _1073320711.unknown _1073320721.unknown _1073320710.unknown _1073320697.unknown _1073320708.unknown _1073320696.unknown _1073320662.unknown _1073320674.unknown _1073320684.unknown _1073320672.unknown _1073320640.unknown _1073320651.unknown _1073320630.unknown _1073320501.unknown _1073320544.unknown _1073320577.unknown _1073320609.unknown _1073320554.unknown _1073320522.unknown _1073320533.unknown _1073320512.unknown _1073320487.unknown _1073320489.unknown _1073320490.unknown _1073320488.unknown _1073320485.unknown _1073320486.unknown _1073320484.unknown

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1629116959.doc ) ( ) ( ) , ( ) ( x f dy y y x k x b a = - ò j l j ) , ( y x k å = = n i i i y q x p y x k 1 ) ( ) ( ) , ( ) ( x p i ) ( y q i b y a b x a £ £ £ £ , ) ( x p i ) ( y q i å ò = = - n i b a i i x f dy y y q x p x 1 ) ( ) ( ) ( ) ( ) ( j l j å …

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