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DR = I ($ identityoperator)if nnoindent $ R n in R f D g ( $ i . e . n h f i l l the Leibniz − Newton formula holds $ : n f r a c f d gf d t g n int ^f t g f a g f ( s ) ds = f ( t )$ forallfunctions $ f $ nnoindent from the space under consideration ) . n h f i l l Moreover , dom $D = RX noplus $ ker $ D . $ n h f i l l Forall $R , R^f nprime g n in $ n begin f a l i g n ∗g n r u l e f3emgf0.4 pt g nendf a l i g n ∗g n centerline f2000 Mathematics Subject Classification : 1 − 0 ,1A55 ,1A60 ,0A20 . g nnoindent Key words and phrases : algebraic analysis , right invertible operator , operational calculus . The paper is in final form and no version of it will be published elsewhere . n [ [ 47 ] n ] 48 .. D period PRZEWORSKA hyphen ROLEWICZ nnoindentR sub D comma48 nquad x in XD comma . PRZEWORSKA Rx minus R− toROLEWICZ the power of prime x in ker D comma i period e period the difference of two primitives of x is a constant period Let nnoindentF sub D = open$ R bracef D Fg in L, sub x 0 openn in parenthesisX , X closing Rx parenthesis− R ^f : n Fprime to theg powerx of 2n in = F$ semicolon ker $ FX D =, kernel $ i D .
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