uzluksiz yadroli fredgol’mning ikkinchi tur tenglamasi

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ur tenglamasini o’rganamiz. endi (a) tenglamaning yadrosi aynigan bo’lmagan holni tekshiramiz. agar funksiya kvadratda uzluksiz bo’lsa, matematik analiz kursida isbotlanadigan veyershtrass teoremasiga asosan, har bir uchun va ga nisbatan yetarli yuqori darajali shunday ko’phad mavjud bo’ladiki, barcha da tengsizlik o’rinli bo’ladi. ravshanki ko’phadning har bir hadi bittasi ga, ikkinchi ga bog’liq bo’lgan ikkita ko’paytuvchining ko’paytmasi sifatida ifodalash mumkin. shu sababli yadroni (1) ko’rinishda yozib olishimiz mumkin. bundagi ifoda da (2) sharni qanoatlantiruvchi uzluksiz funksiya. (1) tenglik yadroni kichik va aynigan yadrolar yig’indisiga ajrtatilganligini ifodalovchi formuladir. (1) ga sosan fredgol’m tenglamani (3) ko’rinishda yozib olamiz, bunda (4) parametrning ixtiyoriy chekli tayin qiymati uchun sonni shunday kichik tanlab olamizki, (5) tengsizlik o’rinli bo’lsin. (2) tengsizlikga asosan demak (3) tenglama (5) ga ko’ra birdan-bir yechimga ega bo’ladi. yadroning rezol’ventasini oraqali belgilab, (3) tenglama yechimini (6) ko’rinishda yozib olamiz. (6) tenglikdagi o’rniga uning qiymati (4) ni olib borib qo’yamiz: ushbu belgilashlarni kiritib, (6) tenglamani …

glama ixtiyoriy uchun yechimga ega bo’lavermaydi, (a) tenglamaning yechimga ega bo’lishi uchun uning ozod hadi qo’shma (c) bir jinsli tenglamaning barcha yechimlariga ortogonal bo’lishi zarur va yetarlidir, yani bunda - (c) tenglamaning barcha chiziqli bog’liq bo’lmagan yechimlari. aynan nolga teng bo’lmagan funksiya, ravshanki bir jinsli (b) tenglamaning va unga qo’shma bo’lgan (c) tenglamaning yechimi bo’ladi. bundan keyin, bir jinsli (yoki unga qo’shma) tenglamaning yechimi deganda aynan noldan farqli yechimini tushunamiz. bir jinsli (b) tenglama yechimlarga ega bo’lgan ning qiymatini, yadroning yoki (b) tenglamaning xos soni, funksiyalarni esa shu yadro yoki tenglamaning xos songa mos xos funksiyalari deyiladi. yuqorida bayon qilinganlarga asosan, yana bir bor ta’kidlab o’tamizki, berilgan xos songa mos chiziqli bog’liq bo’lmagan xos funksiyalarning soni cheklidir. yadroning barcha xos sonlarni to’palami bu yadroning spektri deb ataladi. vol’terra tenglamasi yadrosining spektri bo’sh to’plamdan iborat, aynigan yadroli fredgol’m ikkinchi tur tenglamasining spektri esa chekli sondagi elementlardan iborat. endi (a) tenglamani ko’rinishda …

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1662926144.doc ï ï ï ï î ï ï ï ï í ì = - = - = - ò ò ò ) ( 0 ) ( ) , ( ) ( ) ( 0 ) ( ) , ( ) ( ) ( ) ( ) , ( ) ( c dy y x y k x b y y x k x a fx dy y y x k x b a b a b a y l y j l j j l j ) , ( y x k b x a £ £ b y a £ £ 0 î> x y ) , ( 0 y x k r e < - ) , ( …

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