Sous-espaces biinvariants pour certains shifts pondérés
Annales de l'Institut Fourier, Volume 48 (1998) no. 5, p. 1543-1558

We study the biinvariant subspaces for the usual shift on the weighted spaces

Lω2={fL2(𝕋):fω=n|f(n)|ω2(n)1/2<+},

where ω(n)=(1+n) p ,n0 and ω(n) (1+|n|) p n- + for some integer p1. We show that the analytic part of all biinvariant subspaces is spectral if n2 1 nlogω(-n) diverges, but that this does not hold when n2 1 nlogω(-n) converges.

Nous étudions les sous-espaces biinvariants du shift usuel sur les espaces à poids

Lω2=fL2(𝕋):fω=n|f(n)|ω2(n)1/2<+,

ω(n)=(1+n) p ,n0 et ω(n) (1+|n|) p n- +, pour un certain entier p1. Nous montrons que la trace analytique de tout sous-espace biinvariant est de type spectral, lorsque n2 1 nlogω(-n) diverge, mais que ceci n’est plus valable lorsque n2 1 nlogω(-n) converge.

@article{AIF_1998__48_5_1543_0,
     author = {El-Fallah, O. and Kellay, Karim},
     title = {Sous-espaces biinvariants pour certains shifts pond\'er\'es},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {48},
     number = {5},
     year = {1998},
     pages = {1543-1558},
     doi = {10.5802/aif.1666},
     zbl = {0919.47020},
     mrnumber = {99k:47012},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_1998__48_5_1543_0}
}
El-Fallah, O.; Kellay, Karim. Sous-espaces biinvariants pour certains shifts pondérés. Annales de l'Institut Fourier, Volume 48 (1998) no. 5, pp. 1543-1558. doi : 10.5802/aif.1666. http://www.numdam.org/item/AIF_1998__48_5_1543_0/

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