Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Eigenfunction expansions of ultradifferentiable functions and
  ultradistributions. III. Hilbert spaces and Universality   In this paper we analyse the structure of the spaces of smooth type
functions, generated by elements of arbitrary Hilbert spaces, as a continuation
of the research in our previous papers in this series. We prove that these
spaces are perfect sequence spaces. As a consequence we describe the tensor
structure of sequential mappings on the spaces of smooth type functions and
characterise their adjoint mappings. As an application we prove the
universality of the spaces of smooth type functions on compact manifolds
without boundary.

18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess