Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak $A$-frames and weak $A$-semi-frames   After reviewing the interplay between frames and lower semi-frames, we
introduce the notion of lower semi-frame controlled by a densely defined
operator $A$ or, for short, a \emph{weak lower $A$-semi-frame} and we study its
properties. In particular, we compare it with that of lower atomic systems,
introduced in \cite{GB}. We discuss duality properties and we suggest several
possible definitions for weak $A$-upper semi-frames. Concrete examples are
presented.

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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: econ
32
The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: physics
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: cs