Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A spectral theory of linear operators on rigged Hilbert spaces under
  analyticity conditions   A spectral theory of linear operators on rigged Hilbert spaces (Gelfand
triplets) is developed under the assumptions that a linear operator $T$ on a
Hilbert space $\mathcal{H}$ is a perturbation of a selfadjoint operator, and
the spectral measure of the selfadjoint operator has an analytic continuation
near the real axis in some sense. It is shown that there exists a dense
subspace $X$ of $\mathcal{H}$ such that the resolvent $(\lambda -T)^{-1}\phi$
of the operator $T$ has an analytic continuation from the lower half plane to
the upper half plane as an $X'$-valued holomorphic function for any $\phi \in
X$, even when $T$ has a continuous spectrum on $\mathbf{R}$, where $X'$ is a
dual space of $X$. The rigged Hilbert space consists of three spaces $X \subset
\mathcal{H} \subset X'$. A generalized eigenvalue and a generalized
eigenfunction in $X'$ are defined by using the analytic continuation of the
resolvent as an operator from $X$ into $X'$. Other basic tools of the usual
spectral theory, such as a spectrum, resolvent, Riesz projection and semigroup
are also studied in terms of a rigged Hilbert space. They prove to have the
same properties as those of the usual spectral theory. The results are applied
to estimate asymptotic behavior of solutions of evolution equations.

28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an