Cyclicity of non vanishing functions in the polydisc and in the ball

Eric Amar (1) , Pascal J. Thomas (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 IMT - Institut de Mathématiques de Toulouse UMR5219

We use a special version of the Corona Theorem in several variables, valid when all but one of the data functions are smooth, to generalize to the polydisc and to the ball results obtained by El Fallah, Kellay and Seip about cyclicity of non vanishing bounded holomorphic functions in large enough Banach spaces of analytic functions determined either by weighted sums of powers of Taylor coefficients or by radially weighted integrals of powers of the modulus of the function.

Domaines: Variables complexes [math.CV]

Eric Amar, Pascal J. Thomas. Cyclicity of non vanishing functions in the polydisc and in the ball. 2018. ⟨hal-01959443⟩