Baza Publikacji Pracowników Politechniki Lubelskiej

Status:
Autorzy:	Bobrowski Adam
Rok wydania:	2016
Wersja dokumentu:	Drukowana \| Elektroniczna
Język:	angielski
Wolumen/Tom:	511
Strony:	31 - 53
Impact Factor:	0,973
Web of Science® Times Cited:	4
Scopus® Cytowania:	4
Bazy:	Web of Science \| Scopus \| Web of Science Core Collection
Efekt badań statutowych	NIE
Materiał konferencyjny:	NIE
Publikacja OA:	NIE
Abstrakty:	angielski
	The result that goes essentially back to Euler [15] says that for any element a of a unital Banach algebra A with unit u, the limit lim(epsilon -> 0+)(u + epsilon a)([epsilon-1t]) (where [.] denotes the integral part) exists for all t is an element of R and equals eta. As developed by E. Hille [22, Thm. 12.2.1], in the case where a is replaced by the generator A of a strongly continuous semigroup {e(tA), t >= 0} in a Banach space X, a proper counterpart of this formula is e(tA) = lim(epsilon -> 0+) (I-X - epsilon A)(-[epsilon-1t]) strongly in X. Motivated by an example from mathematical biology (related to Rotenberg's model of cell growth [40]) we study convergence of a similar approximation in which u (resp. I-X) is replaced by j is an element of A (resp. J is an element of L(X)) such that for some l >= 2, j(l) = u (resp. J(l) = I-X). (C) 2016 Elsevier Inc. All rights reserved.

On Hille-type approximation of degenerate semigroups of operators