Affiliation:
1. Dipartimento di Matematica e Informatica Università degli Studi di Palermo Palermo Italy
Abstract
AbstractGiven an arbitrary sequence of elements of a Hilbert space , the operator is defined as the operator associated to the sesquilinear form , for . This operator is in general different from the classical frame operator but possesses some remarkable properties. For instance, is always self‐adjoint with regard to a particular space, unconditionally defined, and, when ξ is a lower semiframe, gives a simple expression of a dual of ξ. The operator and lower semiframes are studied in the context of sequences of integer translates of a function of . In particular, an explicit expression of is given in this context, and a characterization of sequences of integer translates, which are lower semiframes, is proved.
Reference35 articles.
1. Frames and semi-frames
2. Frames, Semi-Frames, and Hilbert Scales
3. Classification of General Sequences by Frame-Related Operators
4. Lower semi‐frames, frames, and metric operators;Antoine J.‐P.;Mediterr. J. Math.,2021
5. An operator based approach to irregular frames of translates;Balazs P.;Mathematics,2019