Holomorphic flows, cocycles, and coboundaries.

Jafari, Farhad; Tonev, Thomas; Toneva, Elena; Yale, Keith

doi:10.1307/mmj/1029005702

Cited by 17 publications

(16 citation statements)

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“…Now, by Theorem 4.3 (ii) in [JTTY,p. 249], since G(z 0 ) = 0, it follows that a is a coboundary if and only if g(z 0 ) = 0.…”

Section: Proof Simply Recall That M(t Z) = Exp(a(t Z))mentioning

confidence: 87%

“…(i) If a is an additive cocycle for the fixed-point-free flow ϕ, G(z) = 0, and since a is continuously differentiable in t by Theorem 2, the result follows from Theorem 4.2 in [JTTY,p. 248].…”

Section: Proof Simply Recall That M(t Z) = Exp(a(t Z))mentioning

confidence: 98%

“…As an immediate extension of this paper, it would be interesting to know if projective cocycles (see [JTTY,Example 5.1 and Proposition 5.2]) are also automatically differentiable. This will help answer the question: Given h ∈ H(G) can one find a nonvanishing weight function p such that m(t, z) = p(t) exp(th(z)) is a cocycle?…”

Section: Open Problemsmentioning

confidence: 99%

See 2 more Smart Citations

Automatic differentiability and characterization of cocycles of holomorphic flows

Jafari

Tonev

Toneva

2005

Proc. Amer. Math. Soc.

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“…Now, by Theorem 4.3 (ii) in [JTTY,p. 249], since G(z 0 ) = 0, it follows that a is a coboundary if and only if g(z 0 ) = 0.…”

Section: Proof Simply Recall That M(t Z) = Exp(a(t Z))mentioning

confidence: 87%

Section: Proof Simply Recall That M(t Z) = Exp(a(t Z))mentioning

confidence: 98%

See 1 more Smart Citation

Automatic differentiability and characterization of cocycles of holomorphic flows

Jafari

Tonev

Toneva

2005

Proc. Amer. Math. Soc.

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“…It was shown in [11,9] that if A = C and the semigroup F has no interior fixed point then each semicocycle can be represented in the form…”

Section: Linearization Of Semicocyclesmentioning

confidence: 99%

Noncommutative Holomorphic Semicocycles

Elin¹,

Jacobzon²,

Katriel³

2019

Michigan Math. J.

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This paper studies holomorphic semicocycles over semigroups in the unit disk, which take values in an arbitrary unital Banach algebra. We prove that every such semicocycle is a solution to a corresponding evolution problem. We then investigate the linearization problem: which semicocycles are cohomologous to constant semicocycles? In contrast with the case of commutative semicocycles, in the non-commutative case non-linearizable semicocycles are shown to exist. Simple conditions for linearizability are derived and are shown to be sharp.

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“…Most of the additional notation used here is standard (see e.g. [4], [6] or [11]). Let H (G) be the set of holomorphic functions on an open domain G ⊂ C and let X ⊆ H (G) be a Banach space of holomorphic functions on G. We suppose that the imbedding X → H (G) is continuous with respect to the respective topologies.…”

mentioning

confidence: 99%