Integral representations of closed operators as bi-Carleman operators with arbitrarily smooth kernels

Details Integral representations of closed operators as bi-Carleman operators with arbitrarily smooth kernels Integral representations of closed operators as bi-Carleman operators with arbitrarily smooth kernels

2004-04-13

arxiv.org/abs/math/0404244v1

Mathematics

Spectral Theory

LaTeX file, 10 pages

Scientific paper

In this paper, we characterize all closed linear operators in a separable
Hilbert space which are unitarily equivalent to an integral bi-Carleman
operator in $L_2(R)$ with bounded and arbitrarily smooth kernel on $R^2$. In
addition, we give an explicit construction of corresponding unitary operators.
The main result is a qualitative sharpening of an earlier result of [5].

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