Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inverse wave scattering in the Laplace domain: a factorization method
  approach   Let $\Delta_{\Lambda}\le \lambda_{\Lambda}$ be a semi-bounded self-adjoint
realization of the Laplace operator with boundary conditions (Dirichlet,
Neumann, semi-transparent) assigned on the Lipschitz boundary of a bounded
obstacle $\Omega$. Let $u^{\Lambda}_{f}$ and $u^{0}_{f}$ denote the solutions
of the wave equations corresponding to $\Delta_{\Lambda}$ and to the free
Laplacian $\Delta$ respectively, with a source term $f$ concentrated at time
$t=0$ (a pulse). We show that for any fixed $\lambda>\lambda_{\Lambda}\ge 0$
and any fixed $B\subset\subset{\mathbb R}^{n}\backslash\bar\Omega$, the
obstacle $\Omega$ can be reconstructed by the data $$
F^{\Lambda}_{\lambda}f(x):=\int_{0}^{\infty}e^{-\sqrt\lambda\,t}\big(u^{\Lambda}_{f}(t,x)-u^{0}_{f}(t,x)\big)\,dt\,,\qquad
x\in B\,,\ f\in L^{2}({\mathbb R}^{n})\,,\ \mbox{supp}(f)\subset B\,. $$ A
similar result holds in the case of screens reconstruction, when the boundary
conditions are assigned only on a part of the boundary. Our method exploits the
factorized form of the resolvent difference
$(-\Delta_{\Lambda}+\lambda)^{-1}-(-\Delta+\lambda)^{-1}$.

26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom