Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Frames of translates with prescribed fine structure in shift invariant
  spaces   For a given finitely generated shift invariant (FSI) subspace $\cW\subset
L^2(\R^k)$ we obtain a simple criterion for the existence of shift generated
(SG) Bessel sequences $E(\cF)$ induced by finite sequences of vectors $\cF\in
\cW^n$ that have a prescribed fine structure i.e., such that the norms of the
vectors in $\cF$ and the spectra of $S_{E(\cF)}$ is prescribed in each fiber of
$\text{Spec}(\cW)\subset \T^k$. We complement this result by developing an
analogue of the so-called sequences of eigensteps from finite frame theory in
the context of SG Bessel sequences, that allows for a detailed description of
all sequences with prescribed fine structure. Then, given $0<\alpha_1\leq
\ldots\leq \alpha_n$ we characterize the finite sequences $\cF\in\cW^n$ such
that $\|f_i\|^2=\alpha_i$, for $1\leq i\leq n$, and such that the fine spectral
structure of the shift generated Bessel sequences $E(\cF)$ have minimal spread
(i.e. we show the existence of optimal SG Bessel sequences with prescribed
norms); in this context the spread of the spectra is measured in terms of the
convex potential $P^\cW_\varphi$ induced by $\cW$ and an arbitrary convex
function $\varphi:\R_+\rightarrow \R_+$.

18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph