Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the differentiability of weak solutions of an abstract evolution
  equation with a scalar type spectral operator on the real axis   Given the abstract evolution equation \[ y'(t)=Ay(t),\ t\in \mathbb{R}, \]
with scalar type spectral operator $A$ in a complex Banach space, found are
conditions necessary and sufficient for all weak solutions of the equation,
which a priori need not be strongly differentiable, to be strongly infinite
differentiable on $\mathbb{R}$. The important case of the equation with a
normal operator $A$ in a complex Hilbert space is obtained immediately as a
particular case. Also, proved is the following inherent smoothness improvement
effect explaining why the case of the strong finite differentiability of the
weak solutions is superfluous: if every weak solution of the equation is
strongly differentiable at $0$, then all of them are strongly infinite
differentiable on $\mathbb{R}$.

14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ