Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Direct and inverse theorems in the theory of approximation by the Ritz
  method   For an arbitrary self-adjoint operator $B$ in a Hilbert space $H$, we present
direct and inverse theorems establishing the relationship between the degree of
smoothness of a vector $x \in H$ with respect to the operator $B$, the rate of
convergence to zero of its best approximation by exponential-type entire
vectors of the operator $B$, and the $k$-modulus of continuity of the vector
$x$ with respect to the operator $B$. The results are used for finding a priori
estimates for the Ritz approximate solutions of operator equations in a Hilbert
space.

18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat