Fonctionnelles causales non linéaires et indéterminées non commutatives

Fliesś, Michel

doi:10.24033/bsmf.1931

Cited by 357 publications

(256 citation statements)

References 9 publications

(14 reference statements)

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“…We thereby obtain the following algebra morphism, denoted by γ • , for the regularization to γ with respect to the quasi-shuffle product independently to the regularization with respect to the shuffle product 19 and then by applying the tensor product of morphisms γ • ⊗ Id on the diagonal series, over Y , we get (see Annexe A) Theorem 11. The mapping γ • realizes the morphism from (Q Y , ) to (R, .)…”

Section: Corollary 4 ([39]mentioning

confidence: 99%

“…19 In [4,8,21,48], the authors suggest the simultaneous regularizations, with respect to the shuffle product and the quasi-shuffle product, to T and then to set T = 0.…”

Section: Corollary 4 ([39]mentioning

confidence: 99%

“…The {Li w } w∈X * are C-linearly independent [35,32]. The 6 The weight is as in Equation (19). 7 See Annexe A, for the study of the Hopf algebra of which is not included in [45].…”

Section: Iterated Integrals and Polylogarithmsmentioning

confidence: 99%

See 2 more Smart Citations

On a conjecture by Pierre Cartier about a group of associators

Minh

2013

Acta Math Vietnam.

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In [8], Pierre Cartier conjectured that for any non commutative formal power series Φ on X = {x0, x1} with coefficients in a Q-extension, A, subjected to some suitable conditions, there exists an unique algebra homomorphism ϕ from the Q-algebra generated by the convergent polyzêtas to A such that Φ is computed from ΦKZ Drinfel'd associator by applying ϕ to each coefficient. We prove ϕ exists and it is a free Lie exponential over X. Moreover, we give a complete description of the kernel of polyzêta and draw some consequences about a structure of the algebra of convergent polyzêtas and about the arithmetical nature of the Euler constant.

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Section: Corollary 4 ([39]mentioning

confidence: 99%

“…19 In [4,8,21,48], the authors suggest the simultaneous regularizations, with respect to the shuffle product and the quasi-shuffle product, to T and then to set T = 0.…”

Section: Corollary 4 ([39]mentioning

confidence: 99%

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On a conjecture by Pierre Cartier about a group of associators

Minh

2013

Acta Math Vietnam.

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“…Numerous topics in control theory uses this point of view (see for example [Fli81,Isi95,Kaw98]). It way also used in the stochastic context to deal with flow of Stochastic Differential Equations (see for example [Yam79, FNC82,BA89,Cas93]... or the book [Bau04]).…”

Section: Lemma 20 For Anymentioning

confidence: 99%

“…Introduced in the 50's by K.-T. Chen (see for example [Che58]), the notion of iterated integrals provides an algebraic tool to deal with a geometrical object which is a smooth path, and allows us to manipulate controlled differential equations using formal computations (see for example [Fli81,Isi95]). …”

Section: Introductionmentioning

confidence: 99%