Extremal problems in the Fock space
This well-written paper investigates some extremal problems in the Fock space. The Fock space, \(F^2\), consists of those entire functions \(f\) for which \(\|f\|_{2}^2=\int_{\mathbb C}|f(z)|^2 e^{-|z|^2}\,dA(z)<\infty, \) where \(dA(z)=\frac{1}{\pi}dxdy\) is the normalized area measure. After an informative introduction, the authors prove some fundamental results (cf. Section 2) pertaining to the order and type of an entire function in the Fock space. In Section 3, they study the zeros of the extremal functions for zero-based subspaces. In addition, the authors solve a Carathéodory-type extremal problem for functions in \(F^2\) (Section 4).
scientific article; zbMATH DE number 5723307
scientific article