Functional models and asymptotically orthonormal sequences.
In the paper under review, a comprehensive treatment of functional models and asymptotically orthonormal sequences is given. In the first two sections, preliminaries and the main facts are presented. For complex Hilbert spaces, the notions of complete, minimal, Riesz and Carleson sequences are given. For an inner function, a model space in a Hardy space of the unit disc is constructed. In the third section, asymptotically orthonormal sequences (AOS) and asymptotically orthonormal basic sequences (AOB) are analysed. Equivalent characterizations for AOB's are given and it is shown that complete AOB's can be obtained by slightly perturbing orthonormal bases. The fourth section is dedicated to the analysis of the reproducing kernels and AOB's, while in the fifth the projection onto a model space is analysed. In the sixth section of the paper, the study of the stability of AOB's with respect to small perturbations is made, and in the seventh section more details about AOB's of exponentials are given. The paper ends with a section giving examples in various cases. A large class of complete AOB's formed by reproducing kernels is obtained.
scientific article; zbMATH DE number 2014685
scientific article