The study reveals a class of counterexamples to de Branges' conjecture, challenging existing notions.
By providing these counterexamples, the research implies the necessity of the continuity property in de Branges spaces.
The approach outlines the failure of certain assumptions made in previous work by L. de Branges.
These findings call for a reevaluation of the axiomatic framework used to describe de Branges spaces.
Abstract
We provide a broad class of counterexamples to a conjecture of L. de Branges concerning the superfluity of the continuity property in the axiomatic description of de Branges spaces.