Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vector-Valued (Super) Weaving Frames   Two frames $\{\phi_{i}\}_{i \in I}$ and $\{\psi_{i}\}_{i \in I}$ for a
separable Hilbert space $H$ are woven if there are positive constants $A \leq
B$ such that for every subset $\sigma \subset I$, the family $\{\phi_{i}\}_{i
\in \sigma} \cup \{\psi_{i}\}_{i \in \sigma^{c}}$ is a frame for $H$ with frame
bounds $A, B$. Bemrose et al. introduced weaving frames in separable Hilbert
spaces and observed that weaving frames has potential applications in signal
processing. Motivated by this, and the recent work of Balan in the direction of
application of vector-valued frames (or superframes) in signal processing, we
study vector-valued weaving frames. In this paper, first we give some
fundamental properties of vector-valued weaving frames. It is shown that if a
family of vector-valued frames is woven, then the corresponding family of
frames for atomic spaces is woven, but the converse is not true. We present a
technique for the construction of vector-valued woven frames from given woven
frames for atomic spaces . Necessary and sufficient conditions for
vector-valued weaving Riesz sequences are given. Several numerical examples are
given to illustrate the results.

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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: cs
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The categories of this paper are: q-bio