Unconditional reproducing kernel bases in de Branges spaces (Q2498310)

If \(E\) is an entire function from the Hermite--Biehler class, then the de Branges space \(\mathcal H(E)\) consists of entire functions \(f\) such that \(f/E\) and \(f^*/E\) are of bounded type and nonpositive mean type in the upper half-plane and \(f/E\) is square integrable on \(\mathbb R\). Here, \(f^*(z)=\bar f(\bar z)\). Using the method of integral norm estimates of resolvents, the authors obtain a criterion which guarantees that the family \(\{k(\cdot,\lambda)\mid\lambda\in\Lambda\}\) of reproducing kernels for \(\mathcal H(E)\) is an unconditional basis of \(\mathcal H(E)\). They obtain also conditions guaranteeing that the special family \(\{k(\cdot, n+i)\mid n\in\mathbb Z\}\) is an unconditional basis. The proofs are not presented. The results of the present paper are closely related to those obtained by \textit{S.\,V.\thinspace Khrushchev, N.\,K.\thinspace Nikolskij} and \textit{B.\,S.\thinspace Pavlov} in [Lect.\ Notes Math.\ 864, 214--335 (1981; Zbl 0466.46018)] in the context of the spaces \(K_\Theta\).