On Hille-type approximation of degenerate semigroups of operators
Artykuł w czasopiśmie
MNiSW
30
Lista A
| 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. |
