Rational Approximation in the Sense of Kato for Transport Semigroups (original) (raw)

The stability of rational approximations of analytic semigroups

BIT, 1993

It is shown that A-acceptable and, more generally, A( )-acceptablerational approximations of bounded analytic semigroups in Banach space are stable. The result applies, in particular, to the Crank-Nicolson method. 1991 Mathematics Subject Classi cation. 65J10, 65M12.

Numerical Semigroups and Applications

RSME Springer Series, 2016

Contents 10 2. Irreducible numerical semigroups 11 2.1. Decomposition of a numerical semigroup into irreducible semigroups 15 2.2. Free numerical semigroups 15 3. Semigroup of an irreducible meromorphic curve 17 3.1. Newton-Puiseux theorem 17 3.2. The local case 27 3.3. The case of curves with one place at infinity 28 4. Minimal presentations 32 5. Factorizations 38 5.1. Length based invariants 38 5.2. Distance based invariants 41 5.3. How far is an irreducible from being prime 43 References 45

Approximation in the Sense of Kato for the Transport Problem

Electronic Journal of Differential Equations, 2009

CITATION 1 READS 17 2 authors: Some of the authors of this publication are also working on these related projects: On the regularizing effect of time-fractional linear problems View project Abstract. Using Chernoff's Theorem, we present an approximation of the family {S(t) : t ≥ 0} that converges in the sense of Kato to the transport semigroup.

Quantum Markov Semigroups and Quantum Flows

It is a great pleasure to thank also R. Soto and the Editorial Board of "Proyecciones" for publication of this unusually lengthy article. 3 k=0 i −k v + i k u, (T x α)(v + i k u) it follows then that (1.2) holds for each v, u ∈ h. 4 implies 3. In fact 4 implies that (1.2) holds for each v, u in the dense subset of h linearly spanned by the total set. This linear span is obviously dense. 3 implies 2. Let (v n) n≥0 , (u n) n≥0 be two sequences of vectors in h such that the sequences (v n) n≥0 , (u n) n≥0 are square-summable. We must show that lim α n≥0 v n , (T x α)u n = n≥0 v n , (T x)u n. To this end, for every ε > 0, take an integer ν such that n>ν u n 2 < ε, n>ν v n 2 < ε. Remark. Notice that, under the assumptions of Theorem A.1, P (t)u = T (t)u for every u ∈ L 2 (IR d ; I C) ∩ C 0 0 (IR d ; IR) and t ≥ 0. In fact P (t) and T (t) are bounded operators coinciding on the dense (in L 2 (IR d ; I C) and C 0 0 (IR d ; IR)) subset C ∞ c (IR d ; IR). We refer to [43] for the proofs of the above results.