A Variation on Selberg's Approximation Problem

Abstract

Let $\alpha \in \mathbb{C}$ in the upper half-plane and let $I$ be an interval. We construct an analogue of Selberg's majorant of the characteristic function of $I$ that vanishes at the point $\alpha$. The construction is based on the solution to an extremal problem with positivity and interpolation constraints.

21 pages. A few typos corrected for version 2

References in corpus (2)

• Bounding $\zeta (s)$ in the critical strip
• Entire approximations for a class of truncated and odd functions

Cited by in corpus (1)

• Extremal functions with vanishing condition