# On the Extension of a Certain Class of Carleman Operators

### S. M. Bahri

Department of Mathematics, Mostaganem, Algeria

## Abstract

The integral operators of Carleman play an important role in the spectral theory of selfadjoint operators and made the object of several works such those of G.~I.~Targonski [{\it Proc. Amer. %%% here the references are put between hooks %%% Math. Soc.} 18 (1967)(3)], %(\cite{T}), V.~B.~Korotkov [{\it Sib. Math.~J.} 11 (1970)(1)], %(\cite{K}) and J.~Weidmann [{\it Manuscripta Math.} (1970)(2)]. %(\cite{W1}). In the present paper, we study a certain class of these operators in the Hilbert space $L^{2}\left(X,\mu\right)$. Precisely, we give necessary and sufficient conditions so that they possess equal defeciency indices. Such operators find their applications in the theory of random variable approximation.

## Cite this article

S. M. Bahri, On the Extension of a Certain Class of Carleman Operators. Z. Anal. Anwend. 26 (2007), no. 1, pp. 57–64

DOI 10.4171/ZAA/1310