Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Formulations of the F-functional calculus and some consequences   In this paper we introduce the two possible formulations of the F-functional
calculus which are based on the Fueter-Sce mapping theorem in integral form and
we introduce the pseudo F-resolvent equation. In the case of dimension 3 we
prove the F-resolvent equation and we study the analogue of the Riesz
projectors associated with this calculus. The case of dimension 3 is also
useful to study the quaternionic version of the F-functional calculus.

13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol