Catherine Bénéteau

Remarks on the Bohr Phenomenon

Bohr’s Theorem [10] states that analytic functions bounded by 1 in the unit disk have power series

The Isoperimetric Inequality via Approximation Theory and Free Boundary Problems

\sum a_n z^n

CYCLICITY IN DIRICHLET-TYPE SPACES AND EXTREMAL POLYNOMIALS

such that

Extremal Problems for Nonvanishing Functions in Bergman Spaces

\sum |a_n||z|^n<1

CYCLICITY IN DIRICHLET-TYPE SPACES AND EXTREMAL POLYNOMIALS II: FUNCTIONS ON THE BIDISK

in the disk of radius 1/3 (the so-called Bohr radius). On the other hand, it is known that there is no such Bohr phenomenon in Hardy spaces with the usual norm, although it is possible to build equivalent norms for which a Bohr phenomenon does occur. In this paper, we consider Hardy space functions that vanish at the origin and obtain an exact positive Bohr radius. Also, following [4, 11], we discuss the growth and Bohr phenomena for series of the type

Extremal Problems in the Fock Space

\sum |a_n|^p r^n

POGIL in the Calculus Classroom

,

Orthogonal polynomials, reproducing kernels, and zeros of optimal approximants

0<p<2

Jensen type inequalities and radial null sets

, that come from functions

A Survey on the Maximal Number of Solutions of Equations Related to Gravitational Lensing

f(z) = \sum a_n z^n