Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orthogonality, density and shift-invariance in the Hardy space approach
  to the RH   A Hardy space approach to the Nyman-Beurling and B\'aez-Duarte criterion for
the Riemann Hypothesis (RH) was introduced in [16]. It states that the RH holds
true if and only if the linear manifold $\mathcal{N}$ generated by a sequence
of functions $(h_k)_{k\geq 2}$ is dense in the Hardy space $H^2$. In this
article we ask the following three questions: $\mathbf{A.}$ How small is the
orthogonal complement of $\mathcal{N}$? $\mathbf{B.}$ Is $\mathcal{N}$ dense in
$H^2$ under a weaker topology? $\mathbf{C.}$ Is the closure of $\mathcal{N}$ a
shift-invariant subspace of $H^2$? We use tools from local Dirichlet spaces,
the de Branges-Rovnyak spaces and the Smirnov class to address these questions.
In particular we prove that $\mathbf{C}$ is equivalent to the RH.

12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph