kuchsiz maxsuslikka ega bo‘lgan integral tenglamalar

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1629203096.doc ) ( ) ( ) , ( ) ( x f dy y y x k x b a = - ò j l j ) ( ) ( ) , ( ) ( y f dt t t x k y b a = - ò j l j ) , ( y x k l y a b ) ( ) ( ) ( ) , ( x f x dy y y x k b a - = ò j j l ) ( ) ( ) , ( ) ( 2 2 2 x f dt t t x k x b a = - ò j l j dy y f y x k x f x f b a ) ( ) , ( ) ( ) ( 2 ò + = l ) ( ) ( ) , ( ) ( x …

n n y x t x h y x k ) 1 ( 1 ) , ( ) , ( a - - - = n n n y x t x h y x k n ) 1 ( 1 a - - n n ) , ( y x k n ò = x a x f dy y y x k ) ( ) ( ) , ( j ) ( ' ), , ( x f y x k x ) , ( x x k x ò = + x a x x f dy y y x k x x x k ) ( ' ) ( ) , ( ) ( ) , ( j j ò = + x a x f dy y y x k x ) ( * ) ( ) , ( * ) ( j j ) …

keltirish mumkinligini ko‘rsatib o‘tamiz. argument uzunligi oraliqdan marta katta bo‘lgan oraliqda o‘zgarsin. bu oraliqda va funksiyalarni quyidagicha aniqlaymiz. agar bo‘lsa xuddi shunga o‘xshash, yadroni kvadratda bo‘lganda deb aniqlab olsak. ushbu tenglikni e’tiborga olsak,(2) sistema fredgol’mning bitta tenglama ko‘rinishda yoziladi. 3. kuchsiz yadroli integral tenglamalar. (3) ko‘rinishga ega bo‘lsa, bunda o‘z argumentlarining uzluksiz (yoki chegaralangan) funksiyasi. bu usuldan ayrim maxsusliklarini yo‘qotishda foydalanish mumkin, chunki iterasiyalangan yadrolar, umuman aytganda, boshlang‘ich yadroga nisbatan siliqroq bo‘ladi agar (3) tipdagi yadro berilgan bo‘lsa, iterasiyalangan yadro ham (3) ko‘rinishda bo‘ladi, faqat son o‘rniga son bo‘ladi. haqiqatan ham, iterasiyalangan yadro uchun tenglikka ega bo‘lamiz. bu ifodani ko‘rinishda yozib olamiz. bu integrallarda mos ravishda almashtirishlarni bajarsak, bu integrallarda har bir , bunda uzluksiz funksiya, ko‘rinishdagi funksiya ekanligi kelib chiqadi. bundan darhol ga ega bo‘lamiz uzluksiz funksiya. matematik induksiya usuli bilan iterasiyalangan yadro uchun tenglikni to‘g’ri deb hisoblasak, yuqoridagi mulohazalarni qaytarish natijasida tenglik o‘rinli bo‘lishiga ishonch hosil qilamiz. etarli …

ng bo‘lib qolsa, vol’terraning birinchi tur integral tenglamasini tekshirishda katta qiyinchiliklarga duch kelinadi. _1073404693.unknown _1073659430.unknown _1073660390.unknown _1073667767.unknown _1073668556.unknown _1073670465.unknown _1073829255.unknown _1073829354.unknown _1073829454.unknown _1073668813.unknown _1073668715.unknown _1073668807.unknown _1073668596.unknown _1073668619.unknown _1073668222.unknown _1073668367.unknown _1073667886.unknown _1073666728.unknown _1073667051.unknown _1073667710.unknown _1073667762.unknown _1073667003.unknown _1073664587.unknown _1073664898.unknown _1073666256.unknown _1073664437.unknown _1073664462.unknown _1073664493.unknown _1073664170.unknown _1073659736.unknown _1073659950.unknown _1073660256.unknown _1073659886.unknown _1073659511.unknown _1073659567.unknown _1073659474.unknown _1073408388.unknown _1073409285.unknown _1073410361.unknown _1073410681.unknown _1073409756.unknown _1073408436.unknown _1073409199.unknown _1073408415.unknown _1073406909.unknown _1073407161.unknown _1073408365.unknown _1073407141.unknown _1073405801.unknown _1073406728.unknown _1073406594.unknown _1073405083.unknown _1073405524.unknown _1073404907.unknown _1073403693.unknown _1073403857.unknown _1073404240.unknown _1073403800.unknown _1073403622.unknown _1073403641.unknown _1073373783.unknown _1073403575.unknown

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1629203096.doc ) ( ) ( ) , ( ) ( x f dy y y x k x b a = - ò j l j ) ( ) ( ) , ( ) ( y f dt t t x k y b a = - ò j l j ) , ( y x k l y a b ) ( ) ( ) ( ) , ( x f x dy y y x k b a - = ò j j l ) ( ) ( ) , ( ) ( 2 2 2 x f dt t t x k x b a = - ò j l j dy y f y x k …

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