Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quaternion Fourier Transform on Quaternion Fields and Generalizations   We treat the quaternionic Fourier transform (QFT) applied to quaternion
fields and investigate QFT properties useful for applications. Different forms
of the QFT lead us to different Plancherel theorems. We relate the QFT
computation for quaternion fields to the QFT of real signals. We research the
general linear ($GL$) transformation behavior of the QFT with matrices,
Clifford geometric algebra and with examples. We finally arrive at wide-ranging
non-commutative multivector FT generalizations of the QFT. Examples given are
new volume-time and spacetime algebra Fourier transformations.

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The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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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: mtrl-th
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The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th