Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Superoscillating sequences and supershifts for families of generalized
  functions   We construct in this paper a large class of superoscillating sequences, more
generally of $\mathscr F$-supershifts, where $\mathscr F$ is a family of smooth
functions (resp. distributions, hyperfunctions) indexed by a real parameter
$\lambda\in \R$. The key model we introduce in order to generate such families
is the evolution through a Schr\"odinger equation $(i\partial/\partial t -
\mathscr H(x))(\psi)=0$ with a suitable hamiltonian $\mathscr H$, in particular
a suitable potential $V$ when $\mathscr H(x) = -(\partial^2/\partial x^2)/2 +
V(x)$. The family $\mathscr F$ is in this case $\mathscr F= \{(t,x) \mapsto
\varphi_\lambda(t,x)\,;\, \lambda \in \R\}$, where $\varphi_\lambda$ is evolved
from the initial datum $x\mapsto e^{i\lambda x}$. Then $\mathscr F$-supershifts
will be of the form $\{\sum_{j=0}^N C_j(N,a) \varphi_{1-2j/N}\}_{N\geq 1}$ for
$a\in \R\setminus [-1,1]$, taking $C_j(N,a)
=\binom{N}{j}(1+a)^{N-j}(1-a)^j/2^N$. We prove the locally uniform convergence
of derivatives of the supershift towards corresponding derivatives of its
limit. We analyse in particular the case of the quantum harmonic oscillator,
which forces us, in order to take into account singularities of the evolved
datum, to enlarge the notion of supershifts for families of functions to a
similar notion for families of hyperfunctions, thus beyond the frame of
distributions.

23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th