Chernoff and Trotter type product formulas
| dc.creator | Neklyudov, A. | |
| dc.date | 2008-03-09 | |
| dc.date.accessioned | 2026-07-07T09:25:53Z | |
| dc.date.available | 2026-07-07T09:25:53Z | |
| dc.description | We consider the abstract Cauchy problem x'=Ax, x(0)=x_0\in D(A) for linear operators A on a Banach space X. We prove uniqueness of the (local) solution of this problem for a natural class of operators A. Moreover, we establish that the solution x(\cdot) can be represented as a limit of sequence F(t/n)^{n} as n\to\infty in the weak operator topology, where a function F:[0,\infty)\to L(X) satisfies F'(0)y=Ay, y\in D(A). As a consequence, we deduce necessary and sufficient conditions that a linear operator C is closable and its closure is a generator of C_0-semigroup. We also obtain some criteria for the sum of two generators of C_0-semigroups to be a generator of C_0-semigroup such that the Trotter formula is valid. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/0803.1283 | |
| dc.identifier | http://arxiv.org/abs/0803.1283 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156558 | |
| dc.subject | Functional Analysis | |
| dc.subject | 34G10, 47D03, 47D60 | |
| dc.title | Chernoff and Trotter type product formulas | |
| dc.type | text |