"Frame-related Sequences in Chains and Scales of Hilbert Spaces"Bellomonte, GiorgiaFrames for Hilbert spaces are interesting for mathematicians but also important for applications e.g. in signal analysis and in physics. Both in mathematics and physics it is often natural to consider a full scale of spaces rather than only a single one. The study is focused on how certain frame-related properties, as completeness or the property of being a (semi-)frame, of a certain sequence in one of the spaces propagate to the other ones in a scale of Hilbert spaces. The result is that not all the properties of a sequence in a space are maintained if we consider it as a sequence in another Hilbert space of a scale. By studying the relationships between the frame-related operators for a sequence as one in different Hilbert spaces of the scale, it has been found that some properties are kept just in some spaces of the scale, other ones are not maintained anywhere else. For example, the upper semi-frame property is preserved in larger spaces, unlike the lower one which is maintained in smaller ones; on the contrary, a sequence cannot be a frame for both two different Hilbert spaces of a certain scale of Hilbert spaces. |
| http://univie.ac.at/projektservice-mathematik/e/talks/Bellomonte_2022-03_Abstract Bellomonte Strobl22.pdf |
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