2025/06/03 by Nikiforos Biehler, Biehler, Nikiforos
Mathematics · #Meromorphic and Entire Functions #Holomorphic and Operator Theory #Algebraic and Geometric Analysis
paper · pdf · doi:10.48550/arxiv.2506.02901
We consider the class of standard weighted Bergman spaces A2α(\mathbbD) and the set SFN(\mathbbT) of simple partial fractions of degree N with poles on the unit circle. We prove that under certain conditions, the simple partial fractions of order N, with n poles on the unit circle attain minimal norm if and only if the points are equidistributed on the unit circle. We show that this is not the case if the conditions we impose are not met, exhibiting a new interesting phenomenon. We find sharp asymptotics for these norms. Additionally we describe the closure of these fractions in the standard weighted Bergman spaces.