A Sharper Bound: New q-Berezin Radius Results

How tightly can you bound an operator's behavior on a reproducing kernel Hilbert space? That's the question behind a new paper from Energma's research partner, Vuk Stojiljković.

Published in Acta Universitatis Sapientiae, Mathematica (Vol. 18, Article 44, 2026), "Refinements of q-Berezin Radius Inequalities" is co-authored with Mehmet Gürdal and Hamdullah Başaran. The paper draws on four tools: the Berezin number, the Berezin–Crawford number, the Berezin norm, and the quantity m̃(P).

The resulting bounds keep their coefficient functions confined to [0, 1]. One bound never exceeds an earlier adapted estimate, across every admissible value of q. The bound built on m̃(P) may go further, proving sharper under an explicit condition.

The paper extends this to operator products via Buzano's inequality, with worked examples confirming the gains. The discipline behind a provable bound isn't so different from the discipline behind reliable software and it's something Energma takes seriously on both fronts.