Some results about inversion formula of functional operator with generalized dilation are given. By means of commutative Banach algebra theory the explicit form of inversion operator is expressed. Some commutative Banach algebras with countable generator systems are constructed, their maximal ideal spaces are investigated.
Vieno funkcinio operatoriaus atvirkštinio operatoriaus formulė
Santrauka. Straipsnyje nagrinėjama vieno apibendrinto operatoriaus apvertimo problema. Naudojantis komutatyviąją Banacho algebros teorija, sudaryta atvirkštinio operatoriaus išreikštinė skaičiavimo formulė. Sukonstruotos kelios komutatyvinės Banacho algebros, kurių generuojančios sistemos yra suskaičiuojamos. Pagrindinėje teoremoje pateiktos būtinos ir pakankamos sąlygos, kad funkcinis operatorius turėtų atvirkštinį.
Plaschinsky, P. (2001). One functional operator inversion formula. Mathematical Modelling and Analysis, 6(1), 138-146. https://doi.org/10.3846/13926292.2001.9637153
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