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

Igor M. Novitskii
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Abstract

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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Igor M. Novitskii. 2004-04-13. Integral representations of closed operators as bi-Carleman operators with arbitrarily smooth kernels. https://arxiv.org/abs/math/0404244

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