Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the construction of large Algebras not contained in the image of the
  Borel map   The Borel map $j^{\infty}$ takes germs at 0 of smooth functions to the
sequence of iterated partial derivatives at 0. It is well known that the
restriction of $j^{\infty}$ to the germs of quasianalytic ultradifferentiable
classes which are strictly containing the real analytic functions can never be
onto the corresponding sequence space. In a recent paper the authors have
studied the size of the image of $j^{\infty}$ by using different approaches and
worked in the general setting of quasianalytic ultradifferentiable classes
defined by weight matrices. The aim of this paper is to show that the image of
$j^{\infty}$ is also small with respect to the notion of algebrability and we
treat both the Cauchy product (convolution) and the pointwise product. In
particular, a deep study of the stability of the considered spaces under the
pointwise product is developed.

17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int