Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized eigenfunctions of relativistic Schroedinger operators in two
  dimensions   Generalized eigenfunctions of the two-dimensional relativistic Schr\"odinger
operator $H=\sqrt{-\Delta}+V(x)$ with $|V(x)|\leq C< x>^{-\sigma}$,
$\sigma>3/2$, are considered. We compute the integral kernels of the boundary
values $R_0^\pm(\lambda)=(\sqrt{-\Delta}-(\lambda\pm i0))^{-1}$, and prove that
the generalized eigenfunctions $\phi^\pm(x,k)$ are bounded on $R_x^2\times\{k |
a\leq |k|\leq b\}$, where $[a,b]\subset(0,\infty)\backslash\sigma_p(H)$, and
$\sigma_p(H)$ is the set of eigenvalues of $H$. With this fact and the
completeness of the wave operators, we establish the eigenfunction expansion
for the absolutely continuous subspace for $H$. Finally, we show that each
generalized eigenfunction is asymptotically equal to a sum of a plane wave and
a spherical wave under the assumption that $\sigma>2$.

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The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat