Frame-Related Sequences in Chains and Scales of Hilbert Spaces

Frames for Hilbert spaces are interesting mathematicians but also important applications in, e.g., signal analysis and physics. In both mathematics physics, it is natural to consider a full scale of spaces, not only single one. this paper, we study how certain frame-related properties sequence in one the such as completeness or property being (semi-) frame, propagate other ones spaces. We link that respective operators, synthesis. start with detailed survey theory chains. Using canonical isomorphism, frame sequences naturally preserved between different show some results can be transferred if original considered—in particular, upper semi-frame kept larger while lower smaller ones. This leads negative result: never two non-trivial, i.e., equal.