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

by    Igor M. Novitskii

Preprint series: 03-17, Reports on Analysis

Igor M. Novitskii

Preprint series: , Reports on Analysis

MSC:
47B38 Operators on function spaces (general)
47G10 Integral operators [See also 45P05]

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].

Keywords: Closed linear operator, integral linear operator, bi-Carleman operator, Carleman kernel, Hilbert-Schmidt operator, Lemari\'e-Meyer wavelet

Upload: 2003-12-05

Update: 2003-12-05


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