Integral representations of unbounded operators by arbitrarily smooth Carleman kernels

Igor M. Novitskii

paper

Integral representations of unbounded operators by arbitrarily smooth Carleman kernels

arXiv:math/0210186

Abstract

In this paper, we give a characterization of all closed linear operators in a separable Hilbert space which are unitarily equivalent to an integral operator in $L_{2} (R)$ with bounded and arbitrarily smooth Carleman kernel on $R^{2}$ . In addition, we give an explicit construction of corresponding unitary operators.

11 pages