On the Infinite Product ofC0-Semigroups

Arendt, Wolfgang; Driouich, A.; El-Mennaoui, O.

doi:10.1006/jfan.1998.3341

Cited by 6 publications

(13 citation statements)

References 12 publications

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“…The following theorem from [2] was proved there in a different way, the authors being apparently unaware of Hasegawa's result.…”

Section: ]) We Say That the Infinite Product T (T) =mentioning

confidence: 99%

“…It is clear that B n 's commute, so that we are in the setup of the first example of Section. 2, i.e., in the setup of [2]. Moreover, since the B n 's are bounded, the generator of the strongly continuous semigroup T n (t) = n k=1 e tB k is A n = n k=1 B k .…”

Section: The Infinite Product Of E Tbn T≥0 Exists and Its Generator Imentioning

confidence: 99%

“…To this end, we present two examples: one involves the question of the existence of infinite products of semigroups [2], the other concerns the existence of a boundary value of a holomorphic semigroup [1] p. 174.…”

mentioning

confidence: 99%

“…Let us consider the question of existence of an infinite product of commuting contraction semigroups. This question was first discussed in Arendt et al [2], a motivating example being the heat semigroup in infinite dimensions introduced by Cannarsa and Da Prato [5]. Let B n , n ≥ 1 be generators of commuting contraction semigroups:…”

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confidence: 99%

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On a somewhat forgotten condition of Hasegawa and on Blackwell’s example

Bobrowski

2015

Arch. Math.

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Abstract. We show, by presenting two examples, that a somewhat forgotten condition of Hasegawa (Proc Jpn Acad 40:262-266, 1964) is useful in proving convergence of operator semigroups, and may be more handy than the standard range condition. Also, we present the semigroup related to Blackwell's example (Ann Math Statist 29:313-316, 1958) as an infinite product of commuting Markov semigroups. Intriguingly, it is hard to find a manageable description of the generator of this semigroup. As a result, it is much easier to prove the existence of the infinite product involved by direct argument than it is to do this using the Trotter-KatoSova-Kurtz-Hasegawa theory.Mathematics Subject Classification. 47D06, 47D09.

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“…The following theorem from [2] was proved there in a different way, the authors being apparently unaware of Hasegawa's result.…”

Section: ]) We Say That the Infinite Product T (T) =mentioning

confidence: 99%

Section: The Infinite Product Of E Tbn T≥0 Exists and Its Generator Imentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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On a somewhat forgotten condition of Hasegawa and on Blackwell’s example

Bobrowski

2015

Arch. Math.

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“…is on the one hand dense in X by the abstract version of the MittagLeffler-Theorem (see [Est84] and [ADEM98]), on the other hand a Fréchet space with obvious seminorms p n,k (x) := k i=0 A i n x . On this Fréchet space all the groups T n are smooth and bounded.…”

Section: Infinite Products Of Semigroupsmentioning

confidence: 99%

Hille-yosida theory in convenient analysis

Teichmann¹

2002

Rev. Mat. Complut.

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A Hille-Yosida Theorem is proved on convenient vector spaces, a class, which contains all sequentially complete locally convex spaces. The approach is governed by convenient analysis and the credo that many reasonable questions concerning strongly continuous semigroups can be proved on the subspace of smooth vectors. Examples from literature are reconsidered by these simpler methods and some applications to the theory of infinite dimensional heat equations are given.

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