Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Every frame is a sum of three (but nottwo) orthonormal bases, and other
  frame representations   We show that every frame for a Hilbert space H can be written as a (multiple
of a) sum of three orthonormal bases for H. A result of N.J. Kalton is included
which shows that this is best possible in that: A frame can be represented as a
linear combination of two orthonormal bases if and only if it is a Riesz basis.
We further show that every frame can be written as a (multiple of a) sum of two
normalized tight frames or as a sum of an orthonormal basis and a Riesz basis
for H. Finally, every frame can be represented as a (multiple of a) average of
two orthonormal bases for a larger Hilbert space.

10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph