JournalszaaVol. 26, No. 1pp. 57–64

On the Extension of a Certain Class of Carleman Operators

  • S. M. Bahri

    Department of Mathematics, Mostaganem, Algeria
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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 L2(X,μ)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