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10. J. Ecalle, Les fonctions r´esurgentes. Tome I: Les alg`ebres de fonctions r´esurgentes, Publ. Math. Orsay 81-05, Universit´e de Paris–Sud, Orsay (1981). ´ 11. J. Ecalle, Les fonctions r´esurgentes. Tome II: Les fonctions r´esurgentes appliqu´ees a ` l’it´eration, Publ. Math. Orsay 81-06, Universit´e de Paris–Sud, Orsay (1981). 12. P. Fatou, Sur les ´equations fonctionnelles, I, Bull. Soc. Math. France 47 (1919), 161–271. 13. P. Fatou, Sur les ´equations fonctionnelles, II, Bull. Soc. Math.

Math. 151 (2000), 35–57. 16. M. Lacey and C. Thiele, Lp estimates on the bilinear Hilbert transform for 2 < p < ∞, Annals Math. 146 (1997), 693–724. 17. M. Lacey and Thiele, C. Weak bounds for the bilinear Hilbert transform on Lp , Documenta Mathematica, extra volume ICM 1-1000, [1997]. 18. M. Lacey and C. Thiele, On Calder´ on’s conjecture, Ann. Math. 149(2) (1999), 475–496. cat 1. Discrete translates, generating functions We will be using the following notations. For a discrete set Λ ⊂ R and f ∈ Lp (R), Λ(f ) stands for the set of translates τλ f (x) = f (x − λ), λ ∈ Λ.

R. Acad. Sci. Paris 324(1) (1997), 987–991. 12. A. Olevskii and A. , J. Fourier Anal. Appl. 10(1) (2004), 93–104. 13. A. Ulanovskii, Sparse systems of functions closed on large sets in R n , J. London Math.

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