793 |
R.: One-parameter semi-groups for linear evolution equations, GTM194
- Engel, Nagel
- 2000
(Show Context)
Citation Context ...m of {T (t) : t ≥ 0}. Thus we want to have T (t) from the C-resolvent by the inverse Laplace transform. For a C0 semigroup {S(t) : t ≥ 0}, the Phragmén inversion formula is known (see Theorem 5.1 in =-=[5]-=- and cf. Phragmén Doetsch inversion in [1]).∫ t 0 S(s)xds = lim n→∞ ∞∑ j=1 (−1)j+1 j! etjnR(jn,A)x for all x in X, where R(jn,A) is the resolvent of the generator A of {S(t) : t ≥ 0}. Inversion formu... |

45 |
Existence families, functional calculi and evolution equations.
- deLaubenfels
- 1994
(Show Context)
Citation Context ...sely defined and has a nonempty resolvent set. However, operators with empty resolvent set may occur in the abstract Cauchy problem, e. g., Petrovsky correct systems of partial differential equations =-=[4]-=-. Since the generator of C-regularized semigroup may have an empty resolvent set, C-regularized semigroup theory can be applied very efficiently to the abstract Cauchy problem for A with an empty reso... |

19 |
The Cauchy problem and a generalization of the Hille-Yosida theorem
- Davies, Pang
- 1987
(Show Context)
Citation Context ...zed semigroup. 1. Introduction This paper is concerned with the study of inversion formula for Csemigroups. The C-regularized semigroup theory has been introduced by Da Prato [2], and Davies and Pang =-=[3]-=-. This is a generalization of strongly continuous semigroups that may be applied to an abstract Cauchy problem on a Banach space X d dt u(t) = Au(t), u(0) = x. Let A : D(A) ⊂ X → X be a closed linear ... |

12 | Laplace Transform Methods for Evolution Equations
- Bäumer, Neubrander
- 1994
(Show Context)
Citation Context ...T (t) from the C-resolvent by the inverse Laplace transform. For a C0 semigroup {S(t) : t ≥ 0}, the Phragmén inversion formula is known (see Theorem 5.1 in [5] and cf. Phragmén Doetsch inversion in =-=[1]-=-).∫ t 0 S(s)xds = lim n→∞ ∞∑ j=1 (−1)j+1 j! etjnR(jn,A)x for all x in X, where R(jn,A) is the resolvent of the generator A of {S(t) : t ≥ 0}. Inversion formula for C-regularized semigroups 167 In the ... |

3 |
Semigruppi regolarizzabili,
- Prato
- 1966
(Show Context)
Citation Context ...tially bounded C-regularized semigroup. 1. Introduction This paper is concerned with the study of inversion formula for Csemigroups. The C-regularized semigroup theory has been introduced by Da Prato =-=[2]-=-, and Davies and Pang [3]. This is a generalization of strongly continuous semigroups that may be applied to an abstract Cauchy problem on a Banach space X d dt u(t) = Au(t), u(0) = x. Let A : D(A) ⊂ ... |

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