Operatori khatti

Operatori khatti, ba fazohoi khatti umumiyat dodani mafhumi tab- dili khatty. Operatori khattii fazoi E gufta funksiyai G(kh)-ro me­nomand, ki baroi hamai kh muayyan buda, qimathoi on elementhoi fazoi khattii E meboshand va sharti zerinro qone megardonad:

G (akh -j- Ru)! = aG(kh) + RG(u), dar on kh va u — elementhoi dilkhohi fazoi E, — adadho. Agar fazohoi E va Ei normironidashuda va buzurgii ||G(kh) ||/[|kh|| mahdud boshad, operatori khattii F-ro ‘mahdud va ||F(x) 11/11 kh||-ro normai on menomand. Misolhoi asosii Operatorhoi kh. dar fazohoi funksionali operatorhoi khat­tii differensialii

F[x(<)] = a₀(t)x(t) + a_x{t)^ +…+

4^ xit) dtⁿ

va operatorhoi khattii integralii

‘tb* -—g—

^F^(^)1 =; §K(t, s)x(s)ds a

ba hisob meravand. Operatori Laplasro hamchun misoli Operatori khattii funksiyai bisyortagyiryobanda muoina kardan mumkin ast. Nazariyai opera­torhoi khatti dar halli bisyor masalahoi fizikai matematiki va matematikai amali istifoda mesha­vad.