Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Frame-related Sequences in Chains and Scales of Hilbert Spaces   Frames 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 natural to consider a full scale of spaces, and
not only a single one. In this paper, we study 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 other spaces in a scale. We
link that to the properties of the respective frame-related operators, like
analysis or synthesis. We start with a detailed survey of the theory of Hilbert
chains. Using a canonical isomorphism the properties of frame sequences are
naturally preserved between different spaces. We also show that some results
can be transferred if the original sequence is considered, in particular that
the upper semi-frame property is kept in larger spaces, while the lower one to
smaller ones. This leads to a negative result: a sequence can never be a frame
for two Hilbert spaces of the scale if the scale is non-trivial, i.e. spaces
are not equal.

36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th