Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterizations of Adjoint Sobolev Embedding Operators for Inverse
  Problems   We consider the Sobolev embedding operator $E_s : H^s(\Omega) \to
L_2(\Omega)$ and its role in the solution of inverse problems. In particular,
we collect various properties and investigate different characterizations of
its adjoint operator $E_s^*$, which is a common component in both iterative and
variational regularization methods. These include variational representations
and connections to boundary value problems, Fourier and wavelet
representations, as well as connections to spatial filters. Moreover, we
consider characterizations in terms of Fourier series, singular value
decompositions and frame decompositions, as well as representations in finite
dimensional settings. While many of these results are already known to
researchers from different fields, a detailed and general overview or reference
work containing rigorous mathematical proofs is still missing. Hence, in this
paper we aim to fill this gap by collecting, introducing and generalizing a
large number of characterizations of $E_s^*$. The resulting compilation can
serve both as a reference as well as a useful guide for its efficient numerical
implementation in practice.

7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org