topologik vektor fazolarda uzluksiz chiziqli operatorlar

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o‘zbekiston respublikasi oliy ta’lim, fan va innovatsiyalar vazirligi termiz davlat pedagogika instituti tabiiy va aniq fanlar fakulteti funksiya nazariyasi fanidan mavzu:“topologik vektor fazolarda uzluksiz chiziqli operatorlar.” himoyaga tavsiya etilsin: tabiiy va aniq fanlar fakulteti dekani __________________ “___”_____2025 -yil kurs ishi himoyaga tavsiya etilsin: matematika va informatika kafedrasi mudiri _________ p.f.f.d. phd “___” _______2025- yil ilmiy rahbar: o’qituvchi: turayev.x.x “___” _______2025- yil bajardi: guruh talabasi: termiz-2025 yil 1 tasdiqlayman kafedra mudiri _____________ «__» _______ 2025 y. kurs ishi (loyiha)ni bajarish yuzasidan topshiriqlar ___________________________________________ fani bo’yicha guruh ______ talaba ________________ rahbar _____________________ topshiriq 1. ishlanadigan loyiha (mavzu)_______________________________________ ________________________________________________________________ ________________________________________________________________ 2. boshlang’ich ma’lumotlar_________________________________________ ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ 3. qo’llanmalar ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ 4. chizma qismining tuzilishi ________________________________________________________________ 1. ________________________________________________________________ 2. ________________________________________________________________ 3. ________________________________________________________________ 4. ______________

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__________________________________________________ 5.yozma qismining tuzilishi ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ 6. qo’shimcha qismining tuzilishi ________________________________________________________________ ________________________________________________________________ 7. kurs (ishi) loyihasini bajarish rejasi_________________________________ rahbar __________________ (imzo) termiz davlat pedagogika instituti kurs ishi (loyihasi)ga mulohaza talaba__________________________________________________________ (ismi va familiyasi) mavzu___________________________________________________________________________________________________________________________ 1. mavzuning dolzarbligini asoslash__________________________________________________________ ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ 2. qismlar bo’yicha bajarilgan ish tavsifnoma (ishning nazariy va amaliy ahamiyati, zamonaviy-ilmiy uslublardan foydalanganligi) ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ 3. muallif ishiga baho (mustaqilligi, intizomliligi va boshqalar) ________________________________________________________________________________________________________________________________________________________________________________________________ ________________________________________________________________ 4. umumiy xulosalar (ishning topshiriqga mos

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kelishi, talab darajasiga javob berishi, himoyaga qo’yilish imkoni) _______________________________________________________________________________________________________________________________«____» _________ 2025 yil rahbar _______________ termiz davlat pedagogika instituti kurs ishi (loyihasi)ga taqriz talaba__________________________________________________________ (ismi va familiyasi) mavzu___________________________________________________________ ______________________________________________________________ 1. mavzuning dolzarbligini asoslash _______________________________________________________________ ________________________________________________________________ 2. ishning tarkibini baholash ________________________________________________________________ ________________________________________________________________________________________________________________________________ 3. mavzuning baholanishi va uning afzallik tomonlarini ko’rsatish ________________________________________________________________ ________________________________________________________________ _______________________________________________________________ 4. ishda foydalanilgan adabiyotlarga baho berish _______________________________________________________________________________________________________________________________ 5.ilmiy munozara yuritish qobiliyatiga baho berish ________________________________________________________________ ________________________________________________________________ 6. xulosa va takliflarning ochiqligi va dalillari asoslanganligi ________________________________________________________________ ________________________________________________________________ 7. jadval va grafiklar, chizmalar sifatiga berilgan baho, ishni rasmiylashtirishning talab darajasiga javob berishi___________________________________________________________ ________________________________________________________________ 8.ishdagikamchiliklar_____________

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__________________________________ ________________________________________________________________ ________________________________________________________________ 9. muallifning qaysi taklifini ishlab chiqarishga joriy etish maqsadga muofiq ________________________________________________________________ ________________________________________________________________ 10. ishning qo’yilgan talab darajasiga mos to’g’risida umumiy xulosa ________________________________________________________________ ________________________________________________________________ taqrizchining (f.i.sh.) ish joyi , unvoni __________________________________ ________________________________________________________________ «__» _________ 2025 yil rahbar _______________ imzo (muxr) tasdiqlayman fakultet dekani ________. _________ termiz davlat pedagogika instituti ________________________ «_________________________________» kafedrasida bajarilgan kurs ishlarini baholash mezonlari ushbu baholash mezonlari kafedra yig’ilishida muxokama qilinib ma’qullangan. b-a №_ «__» _______ 20__ yil kafedra mudiri: ____________________________ mavzu:topologik vektor fazolarda uzluksiz chiziqli operatorlar mundarija: kirish…………………………………………………………………………3 i.bob. topologik vektor fazolarda uzluksiz chiziqli operatorlarni nazariy asoslari ……………….……….…….5 1.1-§ uzluksiz chiziqli operatorlar……………………………….……….……5 1.2-§ teskari operatorlar prinsipi ……………………………….……….……12 1.3-§ normallangan fazoda chiziqli operatorlar………………….……….……17 ii.bob. uzluksiz chiziqli operatorlar va ularning xossalari……………………………….……….……………………… . 21 2.1-§ banax fazosida toʻla uzluksiz operatorlar (yani kompakt operatorlar)…..21 2.2-§ uzluksiz chiziqli operatorlarning tasnifi va misollar…………………….26 xulosa……..………………………………………………………………..30foydalanilgan adabiyotlar ro`yxati……………………….31 kirish mavzuning dolzarbligi. zamonaviy matematik tahlil va funksional analizda topologik vektor fazolar muhim o‘rin …

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differensial tenglamalar, integral tenglamalar va fizikaviy jarayonlar tadqiq qilinadi. ayniqsa, bu fazolarda chiziqli operatorlarning uzluksizligini o‘rganish nazariy hamda amaliy jihatdan muhim ahamiyatga ega. uzluksiz chiziqli operatorlar yordamida turli matematik va fizik muammolarni ifodalash va tahlil qilish imkoniyati tug‘iladi. shu sababli, ushbu mavzuni chuqur o‘rganish va tahlil qilish dolzarb hisoblanadi. topologik vektor fazolar funksional analizning asosiy obyekti bo‘lib, ko‘plab matematik, fizikaviy va muhandislik muammolarini ifodalashda foydalaniladi. ayniqsa, ularning ustida aniqlangan chiziqli operatorlar ko‘plab amaliy va nazariy masalalarda, masalan, integral va differensial tenglamalarni yechishda, optimal boshqaruv, kvant mexanikasi, signalni qayta ishlash kabi sohalarda keng qo‘llaniladi. ushbu operatorlarning uzluksizligi esa muhim tushuncha bo‘lib, ularning barqarorligi, chegaralanganligi, va hal qilinadigan muammolarning to‘g‘ri qo‘yilganligini aniqlashda asosiy rol o‘ynaydi. funksional analiz chekli va cheksiz o‘lchamli fazolarni o‘rganadi. bu fazolarning elementlari funksiyalar, vektorlar, matritsalar, ketma-ketliklar, umuman olganda boshqa matematik ob’ektlardan iborat bo‘lishi mumkin. funksional analizda matematik analiz, funksiyalar nazariyasi va to‘plamlar nazariyasi, algebra va geometriya metodlari, g‘oyalari …

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o‘zbekiston respublikasi oliy ta’lim, fan va innovatsiyalar vazirligi termiz davlat pedagogika instituti tabiiy va aniq fanlar fakulteti funksiya nazariyasi fanidan mavzu:“topologik vektor fazolarda uzluksiz chiziqli operatorlar.” himoyaga tavsiya etilsin: tabiiy va aniq fanlar fakulteti dekani __________________ “___”_____2025 -yil kurs ishi himoyaga tavsiya etilsin: matematika va informatika kafedrasi mudiri _________ p.f.f.d. phd “___” _______2025- yil ilmiy rahbar: o’qituvchi: turayev.x.x “___” _______2025- yil bajardi: guruh talabasi: termiz-2025 yil 1 tasdiqlayman kafedra mudiri _____________ «__» _______ 2025 y. kurs ishi (loyiha)ni bajarish yuzasidan topshiriqlar ___________________________________________ fani bo’yicha guruh ______ talaba ________________ rahbar __________________...

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