2024/12/21 by Beslikas, Athanasios · 2 citations
#30J10 #32A37 #32A40 #Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.2412.16593
In the present article, composition operators induced by Rational Inner Functions on the bidisc \mathbbD2 are studied, acting on the weighted Bergman space A2β(\mathbbD2). We prove that under mild conditions that Rational Inner Functions with one singularity on \mathbbT2 induce unbounded composition operator on A2(\mathbbD2). We also prove that under the condition of stability of the polynomial inducing the Rational Inner Function, the composition operator is bounded between two different Bergman spaces.