Interpolation of analytic functions of moderate growth in the unit disc and zeros of solutions of a linear differential equation

Original · EN

In 2002 A.Hartmann and X.Massaneda obtained necessary and sufficient conditions for interpolation sequences for classes of analytic functions in the unit disc such that M(r,f)=O((1-r)⁻ρ), 0<r<1, ρ∈ (0, +∞), where M(r,f)={ |f(z)|: |z|=r}. Using another method, we give an explicit construction of an interpolating function in this result. As an application we describe minimal growth of the coefficient a such that the equation f''+a(z)f=0 possesses a solution with a prescribed sequence of zeros.