Résumé : The question of extension of (partially defined) operators is ubiquitous in mathematics, physics and computer science. Here, after having dealt with it in general, we explicit concrete computations illustrating cases of unconditional and conditional convergences. This talk provides a collection of techniques coming from Mathematics, Computer Science and Arithmetics.

1. We to recall some of the facts about conc-characters ("Stars of the Plane") and the enlargement of indexations from polynomials to series (especially those who allow a "calculus" i.e. rational ones), from elements to shuffle and stuffle subalgebras.
2. Nuclearity of Hardy spaces
3. Examples of unconditional convergence, partition of indices for the transform of $\frac{log(1+x_0)}{x_0}x_1$ and handling of the "magic identity".

1. In SLC 74 :
   Van Chien Bui, Gérard H.E. Duchamp, Quoc Huan Ngô, Vincel Hoang Ngoc Minh and Christophe Tollu, (Pure) Transcendence Bases in φ-Deformed Shuffle Bialgebras (22 pp.), SLC 74
2. G. H. E. Duchamp and C. Tollu, Sweedler's duals and Schützenberger's calculus , In K. Ebrahimi-Fard, M. Marcolli and W. van Suijlekom (eds), Combinatorics and Physics, p. 67 - 78, Amer. Math. Soc. (Contemporary Mathematics, vol.~539), 2011.
3. https://mathoverflow.net/questions/310354/independence-of-characters-with-respect-to-polynomials
4. G.H.E. Duchamp, Ngo Quoc Hoan, Hoang Ngoc Minh, Kleene stars of the plane, polylogarithms and symmetries, TCS, 800, 2019, 52-72,
   DOI: 10.1016/j.tcs.2019.10.016

Dernière modification : Monday 18 March 2024

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